Multivariate Statistics

This paper is a continuation of the authors' earlier work 1], where a version of the Tr av en's 2] Gaussian clustering neural network (being a recursive counterpart of the EM algorithm) has been investigated. A comparative simulation study of the Gaussian clustering algorithm studied in 1], two versions of plug-in kernel estimators and a version of Friedman's projection pursuit algorithm is presented for two-and threedimensional data. Simulations show that the projection pursuit algorithm is a good or a very good estimator provided, however, that the number of projections is suitably chosen. Although practically con ned to estimating normal mixtures, the simulations con rm general reliability of plug-in estimators and show the same property of the Gaussian clustering algorithm. Indeed, the simulations con rm the earlier conjecture that this last estimator provides a way of e ectively estimating arbitrary and highly structured continuous densities on R d , at least for small d, either by using this estimator itself or, rather, by using it as a pilot estimator for a newly proposed plug-in estimator.

A multivariate extension of the plug-in kernel (and filtered kernel) estimator is proposed and this uses asymptotically optimal bandwidth matrix (matrices) for a normal mixture approximation of a density to be estimated (the filtered kernel estimator uses different matrices for different clusters of data). The normal mixture approximation is provided by a recursive version of the EM algorithm whose initial conditions are in turn obtained via an application of the ideas of adaptive mixtures density estimation and AIC-based pruning. Simulations show that the estimator proposed, while it is in fact a rather complex multistage estimation process, provides a very reliable way of estimating arbitrary and highly structured continuous densities on ~2 and, hopefully, ~3. @ 1997 Elsevier Science B.V.

Background Exposure to cold or hot temperatures is associated with premature deaths. We aimed to evaluate the global, regional, and national mortality burden associated with non-optimal ambient temperatures. In this modelling study, we collected time-series data on mortality and ambient temperatures from 750 locations in 43 countries and five meta-predictors at a grid size of 0•5° × 0•5° across the globe. A three-stage analysis strategy was used. First, the temperature-mortality association was fitted for each location by use of a time-series regression. Second, a multivariate meta-regression model was built between location-specific estimates and meta-predictors. Finally, the grid-specific temperature-mortality association between 2000 and 2019 was predicted by use of the fitted metaregression and the grid-specific meta-predictors. Excess deaths due to non-optimal temperatures, the ratio between annual excess deaths and all deaths of a year (the excess death ratio), and the death rate per 100 000 residents were then calculated for each grid across the world. Grids were divided according to regional groupings of the UN Statistics Division. Globally, 5 083 173 deaths (95% empirical CI [eCI] 4 087 967-5 965 520) were associated with non-optimal temperatures per year, accounting for 9•43% (95% eCI 7•58-11•07) of all deaths (8•52% [6•19-10•47] were coldrelated and 0•91% [0•56-1•36] were heat-related). There were 74 temperature-related excess deaths per 100 000 residents (95% eCI 60-87). The mortality burden varied geographically. Of all excess deaths, 2 617 322 (51•49%) occurred in Asia. Eastern Europe had the highest heat-related excess death rate and Sub-Saharan Africa had the highest cold-related excess death rate. From 2000-03 to 2016-19, the global cold-related excess death ratio changed by -0•51 percentage points (95% eCI -0•61 to -0•42) and the global heat-related excess death ratio increased by 0•21 percentage points (0•13-0•31), leading to a net reduction in the overall ratio. The largest decline in overall excess death ratio occurred in South-eastern Asia, whereas excess death ratio fluctuated in Southern Asia and Europe. Interpretation Non-optimal temperatures are associated with a substantial mortality burden, which varies spatiotemporally. Our findings will benefit international, national, and local communities in developing preparedness and prevention strategies to reduce weather-related impacts immediately and under climate change scenarios.

O trabalho teve como objetivo gerar informações sobre a capacidade combinatória de linhagens de pimentão por meio da análise dialélica multivariada. Foram utilizadas 13 linhagens de pimentão previamente selecionadas com base na reação ao mosaico amarelo do pimentão, sendo oito linhagens com reação do tipo resistência e cinco com reação do tipo suscetibilidade, num dialelo 8 x 5, mais as linhagens parentais. Os 53 tratamentos foram avaliados em estufa em delineamento de blocos casualizados com quatro repetições, sendo avaliadas a produção total e precoce de frutos, massa média de frutos e altura de plantas. A partir dessas quatro características foi realizada a análise dialélica univariada e multivariada. A análise dialélica multivariada apresentou resultados semelhantes às análises dialélicas univariadas, com predominância dos efeitos não-aditivos. Estimativas favoráveis para CGC ocorreram para as características produção total e precoce de frutos nas linhagens PIX-031D-188-14-10 e PIM-013 nos grupos 1 e 2, respectivamente. As linhagens PIX-031D-171-10-10, PIX-031D-188-14-05 e PIM-004 destacaram-se para massa média de frutos e altura de plantas. As estimativas de CEC variaram bastante para as características avaliadas. A utilização da análise dialélica multivariada é uma boa opção para escolha de genitores, pois considera vários caracteres simultaneamente.

Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However, the computation of partial transfer entropy involves high dimensional distributions and thus may not be robust in case of many variables. In this work, different variants of the partial transfer entropy are introduced, by building a reduced number of confounding variables based on different scenarios in terms of their interrelationships with the driving or response variable. Connectivity-based PTE variants utilizing the random forests (RF) methodology are evaluated on synthetic time series. The empirical findings indicate the superiority of the suggested variants over transfer entropy and partial transfer entropy, especially in the case of high dimensional systems. The above findings are further highlighted when applying the causality measures on...

We consider computational methods for evaluating and approximating multivariate chisquare probabilities in cases where the pertaining correlation matrix or blocks thereof have a low-factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a system of MATLAB programs implementing the proposed algorithms. Computer simulations demonstrate the accuracy and the computational efficiency of our methods in comparison with Monte Carlo approximations, and a real data example from statistical genetics illustrates their usage in practice.

Based on the theory of multiple statistical hypothesis testing, we elaborate simultaneous statistical inference methods in dynamic factor models. In particular, we employ structural properties of multivariate chi-squared distributions in order to construct critical regions for vectors of likelihood ratio statistics in such models. In this, we make use of the asymptotic distribution of the vector of test statistics for large sample sizes, assuming that the model is identified and model restrictions are testable. Examples of important multiple test problems in dynamic factor models demonstrate the relevance of the proposed methods for practical applications.

Based on the theory of multiple statistical hypothesis testing, we elaborate simultaneous statistical inference methods in dynamic factor models. In particular, we employ structural properties of multivariate chi-squared distributions in order to construct critical regions for vectors of likelihood ratio statistics in such models. In this, we make use of the asymptotic distribution of the vector of test statistics for large sample sizes, assuming that the model is identified and model restrictions are testable. Examples of important multiple test problems in dynamic factor models demonstrate the relevance of the proposed methods for practical applications.

Epigenetic research leads to complex data structures. Since parametric model assumptions for the distribution of epigenetic data are hard to verify we introduce in the present work a nonparametric statistical framework for two-group comparisons. Furthermore, epigenetic analyses are often performed at various genetic loci simultaneously. Hence, in order to be able to draw valid conclusions for specific loci, an appropriate multiple testing correction is necessary. Finally, with technologies available for the simultaneous assessment of many interrelated biological parameters (such as gene arrays), statistical approaches also need to deal with a possibly unknown dependency structure in the data. Our statistical approach to the nonparametric comparison of two samples with independent multivariate observables is based on recently developed multivariate multiple permutation tests. We adapt their theory in order to cope with families of hypotheses regarding relative effects. Our results indicate that the multivariate multiple permutation test keeps the pre-assigned type I error level for the global null hypothesis. In combination with the closure principle, the family-wise error rate for the simultaneous test of the corresponding locus/parameter-specific null hypotheses can be controlled. In applications we demonstrate that group differences in epigenetic data can be detected reliably with our methodology.

We consider computational methods for evaluating and approximating multivariate chisquare probabilities in cases where the pertaining correlation matrix or blocks thereof have a low-factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a system of MATLAB programs implementing the proposed algorithms. Computer simulations demonstrate the accuracy and the computational efficiency of our methods in comparison with Monte Carlo approximations, and a real data example from statistical genetics illustrates their usage in practice.

] breeding material based on multiple crucial characters is important towards the possible formation of homogeneous groups of genotypes and groups that can be exploited in the identification of parents for use in a breeding program. The objective was to determine the morphological characters that distinguish desirable breeding material and group the genotypes of sorghum according to similarity. Principal component analysis (PCA) and cluster analysis were used to establish the relationships among germplasm and the Shannon Diversity index was used to quantify the level of diversity. The experiment involving 26 sorghum genotypes was conducted at Sussundenga Research Station across two seasons and laid out in a 13 × 2 alpha lattice design with four replications. Cluster analysis grouped genotypes into four clusters based on 15 evaluated traits. Five principal components cumulatively accounting for 58.5% of the total variation were estimated from the PCA analysis. The results showed that genotypes 150B, IS 14257R, LARSVYT 46B, TX 631B, TX 630B and 8601B were the early maturity while for late maturity genotypes were MA 6B, A 6352R, ICSA 19B and MZ 30R. The genotypes IS 7179R, SPL 9B, A 6353R, SPL 38B, SDS 6013R and MZ 2R showed a potential for grain yield improvement. Other genotypes presented potential for drought tolerance and birds attack. The multivariate analyses clearly showed the grouping of the genotypes according to the characters outlined in the study. These results have implications in selecting parents for use in sorghum breeding program.

Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem.

Geostatistical methods are grouped in two main divisions: univariate and multivariate. When there is adequate amount of primary data, univariate methods such as kriging and SGS give a good representation of property distribution in the reservoir, but practical difficulties appear when there is no sufficient data. In such a case it is necessary to choose multivariate geostatistical methods in which some covariables are contributed to model the primary variable. Multivariate geostatistics is a broad term that encompasses all geostatistical methods that utilize more than one variable to predict some physical property of the earth. Bivariate geostatistics is obviously the simplest subset of the multivariate techniques and thus the standard cokriging technique can be called multivariate geostatistics. Cokriging estimates the unsampled value using the primary and secondary variable values from all primary variable sampled locations and also the covariable at an unsampled location, thus there is a need to construct the secondary and cross covariograms. Hence, it is a time-consuming approach. Collocated cokriging is a valuable alternative to full cokriging, which overcomes these problems. It only requires the covariable sample to be available at every location where the principal variable must be estimated. The authors used this in the framework of sequential simulation to produce various realizations. They compare moving average, kriging, and SGS as univariate methods to collocated cokriging and collocated cosimulation as multivariate methods by porosity modeling of an Iranian oil field, although there were only 7 wells available.

Geostatistical methods are grouped in two main divisions: univariate and multivariate. When there is adequate amount of primary data, univariate methods such as kriging and SGS give a good representation of property distribution in the reservoir, but practical difficulties appear when there is no sufficient data. In such a case it is necessary to choose multivariate geostatistical methods in which some covariables are contributed to model the primary variable. Multivariate geostatistics is a broad term that encompasses all geostatistical methods that utilize more than one variable to predict some physical property of the earth. Bivariate geostatistics is obviously the simplest subset of the multivariate techniques and thus the standard cokriging technique can be called multivariate geostatistics. Cokriging estimates the unsampled value using the primary and secondary variable values from all primary variable sampled locations and also the covariable at an unsampled location, thus there is a need to construct the secondary and cross covariograms. Hence, it is a time-consuming approach. Collocated cokriging is a valuable alternative to full cokriging, which overcomes these problems. It only requires the covariable sample to be available at every location where the principal variable must be estimated. The authors used this in the framework of sequential simulation to produce various realizations. They compare moving average, kriging, and SGS as univariate methods to collocated cokriging and collocated cosimulation as multivariate methods by porosity modeling of an Iranian oil field, although there were only 7 wells available.

Most of the existing data mining approaches to time series prediction use data preparation techniques involving an embed of the most recent values of the time series, following the traditional linear auto-regressive methodologies. However, in many time series prediction tasks the alternative approach that uses derivative features constructed from the raw data with the help of domain theories can produce significant prediction improvements. This is particularly noticeable when the available data includes multivariate information but the aim is still the prediction of one particular time series, a situation that occurs frequently in financial time series prediction. This paper presents a method of feature construction based on domain knowledge that uses multivariate time series information and improves the accuracy of next-day stock quotes prediction, when compared with the traditional embed of historical values extracted from the original data.

Physically disabled people experience more restrictions in social activities than healthy people, which are associated with lower level of well-being and poor quality of life (QoL). A cross-sectional study was conducted METHODS: This study was investigated on among 302 eligible physically disabled people. The predictive role of the demographics and clinical characteristics, anxiety and depression, physical activity, and self-efficacy on the 36-Item Short Form Health Survey (SF-36) was examined. Statistical analysis used univariate and multivariate regression models. Gender, self-reported physical activity levels, use of the disability aid tools, and depression were significantly predictors of the physical component summary (PCS) (R 2 = 0.20, P < 0.001). We realized that anxiety, depression, and self-efficacy could significantly predict the mental component summary (MCS) (R 2 = 0.43, P < 0.001). Study results revealed that four and three variables could predict 20% and 43% of PCS and MCS variations, respectively. These findings warranted the detection of QoL risk factors and establishment of targeted interventions to optimize the health-related QoL among physically disabled people.

Analyzing the propagation of uterine electrical activity is poised to become a powerful tool in labor detection and for the prediction of preterm labor. Several methods have been proposed to investigate the relationship between signals recorded externally from several sites on the pregnant uterus. A promising recent method is the multivariate autoregressive (MVAR) model. In this paper we proposed a windowed (time varying) version of the multivariate autoregressive model, called W-MVAR, to investigate the connectivity between signals while still respecting their non-stationary characteristics. The proposed method was tested on synthetic signals as well as applied to real signals. The comparison between the two methods on synthetic signals showed the superiority of W-MVAR to detect connectivity even if it is non-stationary. The application of W-MVAR on multichannel real uterine signals show that the proposed method is a good tool to distinguish non-labor and labor signals. These resul...

The possibility of identifying the provenance of classical marbles and solving related questions, such as the joining fragments problem, via electron spin resonance spectroscopy has been reexamined. The method is based on characterization of the Mn" impurity ubiquitously present in marbles. Six different, although correlated, spectroscopic variables, such as intensity, linewidth, metal hyperfine splitting and others have been measured, together with some petrographic properties, for over 500 samples belonging to 14 different Italian, Greek and Turkish quarrying sites. The work, still in progress, is aimed to establish a marble database including all the historically relevant sites within the Mediterranean basin. The experimental data matrix has been analyzed with the aid of multivariate statistical techniques, primarily linear and quadratic discriminant analysis, and the ability of the method to classify correctly unknown samples has been estimated through standard techniques (resubstitution, jackknife), but also employing control "unknown" samples. The essential result is that, although the all-variables approach may describe the data set very accurately, the predictive power is due to four variables only, which are a suitable combination of spectroscopic and petrographic information. In this way 82.4% of the control samples could be assigned correctly, whereas inclusion of additional variables in the classification rule may result in substantially poorer performance. The conclusion is that ESR spectroscopy, although not providing a complete and general solution for the marble provenance problems, is probably, at the moment, the most developed methodology for identifying marbles. Its results, coupled with artistic historical information, deal correctly with a number of relevant archaeometric problems.

Alzheimer's disease (AD) is known as one of the major causes of dementia and is characterized by slow progression over several years, with no treatments or available medicines. In this regard, there have been efforts to identify the risk of developing AD in its earliest time. While many of the previous works considered crosssectional analysis, more recent studies have focused on the diagnosis and prognosis of AD with longitudinal or time series data in a way of disease progression modeling (DPM). Under the same problem settings, in this work, we propose a novel computational framework that can predict the phenotypic measurements of MRI biomarkers and trajectories of clinical status along with cognitive scores at multiple future time points. However, in handling time series data, it generally faces with many unexpected missing observations. In regard to such an unfavorable situation, we define a secondary problem of estimating those missing values and tackle it in a systematic way by taking account of temporal and multivariate relations inherent in time series data. Concretely, we propose a deep recurrent network that jointly tackles the four problems of (i) missing value imputation, (ii) phenotypic measurements forecasting, (iii) trajectory estimation of cognitive score, and (iv) clinical status prediction of a subject based on his/her longitudinal imaging biomarkers. Notably, the learnable model parameters of our network are trained in an end-to-end manner with our circumspectly defined loss function. In our experiments over The Alzheimer's Disease Prediction Of Longitudinal Evolution (TADPOLE) challenge cohort, we measured performance for various metrics and compared our method to competing methods in the literature. Exhaustive analyses and ablation studies were also conducted to better confirm the effectiveness of our method.

Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder that has recently seen serious increase in the number of affected subjects. In the last decade, neuroimaging has been shown to be a useful tool to understand AD and its prodromal stage, amnestic mild cognitive impairment (MCI). The majority of AD/MCI studies have focused on disease diagnosis, by formulating the problem as classification with a binary outcome of AD/MCI or healthy controls. There have recently emerged studies that associate image scans with continuous clinical scores that are expected to contain richer information than a binary outcome. However, very few studies aim at modeling multiple clinical scores simultaneously, even though it is commonly conceived that multivariate outcomes provide correlated and complementary information about the disease pathology. In this article, we propose a sparse multi-response tensor regression method to model multiple outcomes jointly as well as to model multiple voxels of an image jointly. The proposed method is particularly useful to both infer clinical scores and thus disease diagnosis, and to identify brain subregions that are highly relevant to the disease outcomes. We conducted experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and showed that the proposed method enhances the performance and clearly outperforms the competing solutions.

Alzheimer&#39;s disease (AD) is a progressive and irreversible neurodegenerative disorder that has recently seen serious increase in the number of affected subjects. In the last decade, neuroimaging has been shown to be a useful tool to understand AD and its prodromal stage, amnestic mild cognitive impairment (MCI). The majority of AD/MCI studies have focused on disease diagnosis, by formulating the problem as classification with a binary outcome of AD/MCI or healthy controls. There have recently emerged studies that associate image scans with continuous clinical scores that are expected to contain richer information than a binary outcome. However, very few studies aim at modeling multiple clinical scores simultaneously, even though it is commonly conceived that multivariate outcomes provide correlated and complementary information about the disease pathology. In this article, we propose a sparse multi-response tensor regression method to model multiple outcomes jointly as well as t...

Anomalies in univariate time series often refer to abnormal values and deviations from the temporal patterns from majority of historical observations. In multivariate time series, anomalies also refer to abnormal changes in the inter-series relationship, such as correlation, over time. Existing studies have been able to model such inter-series relationships through graph neural networks. However, most works settle on learning a static graph globally or within a context window to assist a time series forecasting task or a reconstruction task, whose objective is not tailored to explicitly detect the abnormal relationship. Some other works detect anomalies based on reconstructing or forecasting a list of inter-series graphs, which inadvertently weakens their power to capture temporal patterns within the data due to the discrete nature of graphs. In this study, we propose DyGraphAD, a multivariate time series anomaly detection framework based upon a list of dynamic inter-series graphs. The core idea is to detect anomalies based on the deviation of inter-series relationships and intra-series temporal patterns from normal to anomalous states, by leveraging the evolving nature of the graphs in order to assist a graph forecasting task and a time series forecasting task simultaneously. Our numerical experiments on real-world datasets demonstrate that DyGraphAD has superior performance than baseline anomaly detection approaches.

This study checks the hypothesis that sustainable well-being is a determinant factor of fertility through the application of a multiversal method based on the assumptions of Vibration of Effects (VoE) model of multiversal sampling on the Italian Equitable and Sustainable Well-being (BES) dataset. For 48 social indicators of well-being, adopting the Province as statistical unit, the estimate of linear effect has been systematically sampled 1,024 times. This multiversal sampling allows to estimate the component of the hypothetical variability of the estimate of the effect size that depends on the theoretical choices of the analysis. This component is commonly underestimated, hidden, or ignored in regular multivariate analysis or classical bootstrapping. Results do not allow to claim that any of the 48 social indicators is a robust linear predictor of fertility. Indicators associated with high statistical significance are also at risk of misleading the causal relationship. Implications for policy-making and the future direction of the research on BES are discussed in the conclusive remarks.

This study checks the hypothesis that sustainable well-being is a determinant factor of fertility through the application of a multiversal method based on the assumptions of Vibration of Effects (VoE) model of multiversal sampling on the Italian Equitable and Sustain-able Well-being (BES) dataset. For 48 social indicators of well-being, adopting the Province as statistical unit, the estimate of linear effect has been systematically sampled 1,024 times. This multiversal sampling allows to estimate the component of the hypothetical variability of the estimate of the effect size that depends on the theoretical choices of the analysis. This component is commonly underestimated, hidden, or ignored in regular multivariate analysis or classical bootstrapping. Results do not allow to claim that any of the 48 social indicators is a robust linear predictor of fertility. Indicators associated with high statistical significance are also at risk of misleading the causal relationship. Implication...

Deoxyribonucleic acid, more commonly known as DNA, is a fundamental genetic material in all living organisms, containing thousands of genes, but only a subset exhibit differential expression and play a crucial role in diseases. Microarray technology has revolutionized the study of gene expression, with two primary types available for expression analysis: spotted cDNA arrays and oligonucleotide arrays. This research focuses on the statistical analysis of data from spotted cDNA microarrays. Numerous models have been developed to identify differentially expressed genes based on the red and green fluorescence intensities measured using these arrays. We propose a novel approach using a Gaussian copula model to characterize the joint distribution of red and green intensities, effectively capturing their dependence structure. Given the right-skewed nature of the intensity distributions, we model the marginal distributions using gamma distributions. Differentially expressed genes are identified using the Bayes estimate under our proposed copula framework. To evaluate the performance of our model, we conduct simulation studies to assess parameter estimation accuracy. Our results demonstrate that the proposed approach outperforms existing methods reported in the literature. Finally, we apply our model to Escherichia coli microarray data, illustrating its practical utility in gene expression analysis.

The study examines the dynamic dependence structure between the Indian market and other emerging and developed Asia-Pacific markets, a symbol of India's growing economic connectivity with the global. We used the Copulabased Multivariate GARCH model to analyze the Conditional Correlation by Multivariate Generalized Autoregressive Conditional Heteroskedastic (MGARCH) and copula models to determine dependency. The study considered daily indices data from March 04, 2003, to December 31, 2023. The study found that there is a significant dynamic dependency among the Indian market and other Asia-Pacific markets. Compared to findings obtained from static models, our results offer investors interested in the Indian market with more timely recommendations for risk management, international asset allocation, and portfolio diversification.

Diabetes Mellitus is a metabolic disease caused by increased levels of glucose or blood sugar. Diabetes Mellitus is divided into three different types: type I diabetes, type II diabetes, and gestational diabetes or diabetes during pregnancy. Type 2 diabetes mellitus affects 90-95% of diabetics. The aim of this research is to identify related factors that influence Type II Diabetes Mellitus by applying the Multivariate Adaptive Regression Spline (MARS) Method. The model with the lowest Generalized Cross-Validation (GCV) score among the models constructed is considered the best model. The research findings show that BF=10, MI=3, and MO=0 are the optimal parameter combinations for the MARS model with a GCV value of 0,09582998 . According to research using MARS, the predictor variables with an 89.33% classification accuracy that affect the blood glucose levels of Type II Diabetes Mellitus patients include Age (X 1 ), Gender (X 2 ), Blood Pressure (X 3 ), and Comorbidities (X 5 ).

This study aims to identify the spatial variation of air pollutant and its pattern in the northern part of Peninsular Malaysia for four years monitoring observation (2008-2011) based on the seven air monitoring stations. Air pollutant variables that used in this study were Nitrogen Dioxide (NO2), Ozone (O3), Carbon Monoxide (CO), and Particulate Matter (PM10) data and had been supplied by Department Of Environment Malaysia (DOE). ANOVA, environmetric techniques (HACA and Descriptive Analysis) and Artificial Neural Network (ANN) approach were used in data analysed. According to ANOVA single test, significance p-value of PM10 (p= 2.5E-268) is smaller than significance alpha level (p=0.05) and it suitable parameter for further analysis in construct the prevention actions compared to O3, NO2 and CO. HACA categorized seven air monitoring station into three cluster group of station such as High Concentrated Site (HCS), Moderate Concentrated Site (MCS), and Low Concentrated Site (LCS). Des...

Objective: To establish a noticeable and a justifiable identification system to assess the impact of shodhana (processing) on various levels of Baliospermum montanum (Danti) root samples obtained through shodhana (processing technique) in quality agreement based on near-infrared-spectroscopy.Methods: Authenticated raw Danti (R. D) root and various Danti root samples obtained after shodhana (processing) such as water processed Danti root (WPDR), Kusha processed Danti root (KPDR) and classical processed Danti root (CPDR), were dried, pulverized and shifted through eighty meshes. The samples were subjected to NIR spectral detection from 750 to 2500 nm at the interval of 1 nm. The multivariate analysis, principal component analysis (PCA) and hierarchical cluster analysis (HCA) analyzed with the help of Unscrambler and Matlab software.Results: Direct spectral analysis indicated the existence of significant numerical and graphical differences between Danti root samples containing differen...

When testing and recording water quality data from treatment plants, errors arise. The errors are in the form of recordings left blank (missing values), obvious errors in writing or typing, or they can be as a result of values being very small to detect and are therefore censored. The censored values are known to be below the limit of detection (LOD). In statistical analysis, the blank cells can be filled with a certain value. Censored values are often corrected by substituting with a constant value throughout. This value will be a fraction of the limit of detection and most commonly used fractions are, half the limit of detection, the limit of detection divided by the square root of 2, or multiplying the limit of detection by 0.75. The direct substitution method for handling missing and values below the limit of detection results in a uniform distribution for values below the limit of detection, and a true distribution for those above. As a result, treatment of the values below the...

This study evaluated the multivariate relationship among the crude protein (CP) intake and digestibility, the neutral detergent fiber (NDF) intake and digestibility, and the nitrogen excretion in hair sheep fed Mombasa grass silage mixed with açai palm seeds using canonical correlation analysis (CCA). For this purpose, a dataset was constructed using the information derived from a metabolic experiment with Santa Ines sheep (BW ± SE: 33.9 ± 1.37 kg) allocated into a 5 × 5 Latin square. The following two multivariate relationships were explored using CCA: (1) the N in both feces (N feces ) and urine (N urine ) (canonical variate U) versus the intake of both CP (CPI) and NDF (NDFI) (canonical variate V). (2) the N feces and N urine (canonical variate W) versus the digestibility of both CP (CPD) and NDF (NDFD) (canonical variate Z). Canonical loadings for relationship No. 1 revealed that N feces (0.971) and N urine (-0.249) had a positive and negative correlation, respectively, with U. Both CPI (0.960) and NDFI (0.997) had a positive and similar correlation with V. Regarding relationship No. 2, both N feces (0.860) and N urine (0.500) had a positive correlation with W. Conversely, both CPD (-0.910) and NDFD (-0.889) had a negative and similar association with Z. In conclusion, our data showed that when a multivariate approach is used, an increase in both CPI and NDFI produces an increase in N feces , as well as a decrease in N urine . Additionally, a decrease in both CPD and NDFD produces an increase in both N feces and N urine .

High-field 31 P NMR (202.2 MHz) spectroscopy was applied to the analysis of 59 samples from three grades of olive oils, 34 extra virgin olive oils from various regions of Greece, and from different olive varieties, namely, 13 samples of refined olive oils and 12 samples of lampante olive oils. Classification of the three grades of olive oils was achieved by two multivariate statistical methods applied to five variables, the latter being determined upon analysis of the respective 31 P NMR spectra and selected on the basis of one-way ANOVA. The hierarchical clustering statistical procedure was able to classify in a satisfactory manner the three olive oil groups. Subsequent application of discriminant analysis to the five selected variables of oils allowed the grouping of 59 samples according to their quality with no error. Different artificial mixtures of extra virgin olive oil-refined olive oil and extra virgin olive oil-lampante olive oil were prepared and analyzed by 31 P NMR spectroscopy. Subsequent discriminant analysis of the data allowed detection of extra virgin olive oil adulteration as low as 5% w/w for refined and lampante olive oils. Further application of the classification/prediction model allowed the estimation of the percent concentration of refined olive oil in six commercial blended olive oils composed of refined and virgin olive oils purchased from supermarkets.

The statistical analysis of circular, multivariate circular, and spherical data is very important in different areas, such as paleomagnetism, astronomy and biology. The use of nonnegative trigonometric sums allows for the construction of flexible probability models for these types of data to model datasets with skewness and multiple modes. The R package CircNNTSR includes functions to plot, fit by maximum likelihood, and simulate models based on nonnegative trigonometric sums for circular, multivariate circular, and spherical data. For maximum likelihood estimation of the models for the three different types of data an efficient Newton-like algorithm on a hypersphere is used. Examples of applications of the functions provided in the CircNNTSR package to actual and simulated datasets are presented and it is shown how the package can be used to test for uniformity, homogeneity, and independence using likelihood ratio tests.

Loss functions proposed for nonmetric unfolding are discussed critically. Practical experience suggests that they do not work, mathematical reasons are sought why this is. Although the loss functions are constructed in such a way that they are ill-behaved at trivial solutions, it is shown that they are rather well-behaved along differentiable paths to trivial solutions. It is shown that in the neighborhood of trivial solutions we can find infinitely many nonmetric unfolding solutions which cannot be distinguished from stationary points, and which can differ very considerably in loss function value. The conclusion is that nonmetric unfolding, as currently formalized, is an inherently ill-posed problem and that a different approach is called for. This paper originally appeared as a technical report of the Department of Data Theory, University of Leiden, in May 1983. It was never published.

Polynomial component and factor analysis are defined. Algorithms, based on multidimensional array approximation methods, to fit a model with a single common factor to observed multivariate cumulants are described and applied to a psychometric example. Software in R is included.

In this paper it is argued that all multivariate estimation methods, such as OLS regression, simultaneous linear equations systems and, more widely, what are known as LISREL methods, have merit as geometric approximation methods, even if the observations are not drawn from a multivariate normal parent distribution and consequently cannot be viewed as ML estimators. It is shown that for large samples the asymptotical distribution of any estimator, being a totally differentiable covariance function, may be assessed by the δ method. Finally, we stress that the design of the sample and a priori knowledge about the parent distribution may be incorporated to obtain more specific results.It turns out that some fairly traditional assumptions, such as assuming some variables to be non‐random, fixed over repeated samples, or the existence of a parent normal distribution, may have dramatic effects on the assessment of standard deviations and confidence bounds, if such assumptions are not reali...

Polynomial component and factor analysis are de-fined. Algorithms, based on multidimensional array approxi-mation methods, to fit a model with a single common factor to observed multivariate cumulants are described and applied to a psychometric example. Software in R is included.

A model for predicting student performance on introductory programming modules is presented. The model uses attributes identified in a study carried out at four third-level institutions in the Republic of Ireland. Four instruments were used to collect the data and over 25 attributes were examined. A data reduction technique was applied and a logistic regression model using 10-fold stratified cross validation was developed. The model used three attributes: Leaving Certificate Mathematics result (final mathematics examination at second level), number of hours playing computer games while taking the module and programming self-esteem. Prediction success was significant with 80% of students correctly classified. The model also works well on a per-institution level. A discussion on the implications of the model is provided and future work is outlined.

Degree of morphological difference between queens and workers is an important characteristic used to infer the mechanism of caste determination and levels of reproductive conflict in insect societies. In the polistine wasps, the degree of morphological caste difference varies widely, ranging from absent to highly distinct. A lack of obvious caste differences would indicate that most females are totipotent (Strassmann et al. 2002, Mateus 2005), which predicts that reproductive conflict will be higher than in species with well-defined caste roles. For Neotropical swarm-founding polistine wasps (tribe: Epiponini), West-Eberhard (1978, 1981) suggested that castes may be post-imaginally determined in some species. Indeed, female reproductives resemble non-reproductives in morphology in a number of species, and this pattern has been found in Parachartergus Ihering, 1904 (Mateus et al. 1997;

A quantitative structure-property relationship (QSPR) study is suggested for the prediction of retention times of volatile organic compounds. Various kinds of molecular descriptors were calculated to represent the molecular structure of compounds. Modeling of retention times of these compounds as a function of the theoretically derived descriptors was established by multiple linear regression (MLR) and artificial neural network (ANN). The stepwise regression was used for the selection of the variables which gives the best-fitted models. After variable selection ANN, MLR methods were used with leave-one-out cross validation for building the regression models. The prediction results are in very good agreement with the experimental values. MLR as the linear regression method shows good ability in the prediction of the retention times of the prediction set. This provided a new and effective method for predicting the chromatography retention index for the volatile organic compounds.

A new implemented quantitative structure-property relationships (QSPR) method, whose descriptors achieved from bidimensional images, was suggested for the predicting of acidity constant (pK a ) of various acid. The resulted descriptors were subjected to principal component analysis (PCA) and the most significant principal components (PCs) were extracted. Multivariate image analysis applied to QSPR modeling was done by means of principal component-least squares support vector machine (PC-LSSVM) methods. The resulted model showed high prediction ability with root mean square error of prediction of 0.0195 for PC-LSSVM.

In this paper it was investigated if any genotypic footprints from the fat mass and obesity associated (FTO) SNP could be found in 600 MHz 1 H CPMG NMR profiles of around 1,000 human plasma samples from healthy Danish twins. The problem was addressed with a combination of univariate and multivariate methods. The NMR data was substantially compressed using principal component analysis or multivariate curve resolution-alternating least squares with focus on chemically meaningful feature selection reflecting the nature of chemical signals in an NMR spectrum. The possible existence of an FTO signature in the plasma samples was investigated at the subject level using supervised multivariate classification in the form of extended canonical variate analysis, classification tree modeling and Lasso (L1) regularized linear logistic regression model (GLMNET). Univariate hypothesis testing of peak intensities was used to explore the genotypic effect on the plasma at the population level. The multivariate classification approaches indicated poor discriminative power of the metabolic profiles whereas univariate hypothesis testing provided seven spectral regions with p \ 0.05. Applying false discovery rate control, no reliable markers could be identified, which was confirmed by test set validation. We conclude that it is very unlikely that an FTO-correlated signal can be identified in these 1 H CPMG NMR plasma metabolic profiles and speculate that high-throughput untargeted genotype-metabolic correlations will in many cases be a difficult path to follow.