BHEP Class of Tests for Multivariate Normality: An Empirical Comparison

This paper compares the empirical power performances of eight tests for multivariate normality classified under Baringhaus-Henze-Epps-Pulley (BHEP) class of tests. The tests are compared under eight different alternative distributions. The result shows that the eight statistics have good control over type-I-error. Also, some tests are more sensitive to distributional differences with respect to their power performances than others. Also, some tests are generally more powerful than others. The generally most powerful ones are therefore recommended.

A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

On a Vector-Valued Measure of Multivariate Skewness

The canonical skewness vector is an analytically simple function of the third-order, standardized moments of a random vector. Statistical applications of this skewness measure include semiparametric modeling, independent component analysis, model-based clustering, and multivariate normality testing. This paper investigates some properties of the canonical skewness vector with respect to representations, transformations, and norm. In particular, the paper shows its connections with tensor contraction, scalar measures of multivariate kurtosis and Mardia’s skewness, the best-known scalar measure of multivariate skewness. A simulation study empirically compares the powers of tests for multivariate normality based on the squared norm of the canonical skewness vector and on Mardia’s skewness. An example with financial data illustrates the statistical applications of the canonical skewness vector.

Comparison of Four MANOVA Test Statistic for Pig Production in Delta State, Nigeria

This study used the multivariate analysis of variance (MANOVA) test statistic to examine the impact of three categories feed used in the production of pig in Delta State. The multivariate test statistic considered are the Pillai – Bartlett trace, Wilks’ Test Statistic, Roy’s Largest Root Test Statistic, and the Lawley- Hotelling (LH) Statistic. The objectives include to: evaluate the robustness of the four Multivariate Analysis of Variance test statistics to ensure that the best is employed in multivariate analysis to guarantee most useful result in pig production; determine the relatively efficient test statistic for pig production; and determine the test statistic that is consistent across the sample sizes. Secondary source of data collection was used to obtain the data required for the analysis. The outcome of the study showed that the obtained data was multivariate normally distributed based on the result of the asymmetry-based multivariate normality test and the multivariate normality test based on the kurtosis test which makes the data suitable parametric multivariate method such as multivariate analysis of variance (MANOVA). The results show that the Wilks and Roy tests found a significant difference for the intercept. While the Pillai and LH tests could not find any significance. The Roy test was also found to be significant for feed one, feed two, and feed three. The Wilks and Roy tests also turned out to be significant differences for the intercept. All test measures showed significance for feed one. The Wilks and Roy tests also showed a significant difference for feed two, while all test measures found a significance for feed one. Another result showed that none of the tests found significance for the interaction between feed one and two, while the Roy test found significance for the interaction between feed one and three, feed two and three and feed one, two and three. The performance of the test for evaluating the performance of feeds for pig production with/without considering interactions was found to be in the following order of magnitude: Roy, Wilks and Pilla = LH. This result implies that the Roy method, with or without consideration of the interaction, has a better performance of the test than the other methods considered in the study.

Replicability of the Questionnaire Assessing the Addition of IN NATURA Vegetable Oil to the Child’s Diet

Objective: To verify the replicability of the questionnaire Assessing the Addition of IN NATURA Vegetable Oil to the Child’s Diet”. Study design: observational cross-sectional study. Place and Duration of Study: The study was carried out in two pediatric outpatient clinics, one of which refers to a health plan operator (SJM), municipality of São João de Meriti (RJ) and the other, at the Polyclinic Piquet Carneiro of the University from the State of Rio de Janeiro (PPC/UERJ), municipality of Rio de Janeiro (RJ), from March 2017 to January 2019. Sample: Responsible for children feeding, that is, those who buy the food prepare it or serve meals. SJM, n=150 and PPC/UERJ; n=150. Methodology: Doornik-Hansen test verified the Multivariate normality of the scores distribution of the items according to Likert scale. Kaiser-Meyer-Olkin was used as a criterion for identify the adequately of sample for the data adjustment. Conbrach's alpha indicated the internal consistency (coherence) between items on each dimension. The reproducibility by reliability was tested by test-retest by using the weighted Kappa coefficient. Results: Multivariate normality of the SJM scores: (chi2 (22)=602.969 Prob chi2=.0000) and PPC/UERJ: (chi2(22)=411.666 Prob chi2=.0000), adequacy of the samples, KMO: SJM=0.78 to 0.92 and PPC/UERJ=0.76 to 0.92, internal consistency of dimensions (Dimension 1 and 2) by Cronbach's alpha greater than 0.75 for SJM and PPC/UERJ, reproducibility of the questionnaire by weighted Kappa: 0.90 (p value.008), t test for two independent samples, SJM and PPC/UERJ: significant difference for Dimension 1, but not for Dimension 2.

A Comment on Affine Invariance and Ancillarity in Testing Multivariate Normality

With the aim to clarify some confusion apparently still present in part of the literature on testing for multivariate normality, we collect and discuss some facts on invariance and ancillarity of various variants of, so-called, configuration of a multivariate normal sample. In particular, we show how the choice of the rotation matrix, used in the definition of the configuration, influences its invariance, distribution and ancillarity.

Influence of Determinants of Diabetes on Sexual Quality using Discriminant Functions

This paper seeks to give a better understanding of the influence of age, creatinine level, duration of diabetes, glucose level and pulse rate on diabetic-induced sexual dysfunction among people. The study employed two-way MANOVA with balanced samples of 115 each. Prior to the analysis, univariate and multivariate normality, linearity, equality of error and covariance matrices, and multicollinearity assumptions were satisfied. Significance was attained for both sex and marital status (P < 0.05), though their interaction effect was not significant (P > 0.05). Wald’s test for individual groups confirmed the hypothetical decision of MANOVA, though independent T2 failed to report significance for marital status. Under the parameter estimation, it was ascertained that the difference between the groups was in terms of age and creatinine levels of people. The model is also considered credible since bootstrap estimates converged to the empirical estimates. Even though this paper did not exhaust all metabolic and comorbid factors relating to diabetes, it is hoped that it provides an insight into some circumstances in the evolution of diabetes.