Assessing the assumption of multivariate normality is required by many parametric mul- tivariate statistical methods, such as MANOVA, linear discriminant analysis, principal component analysis, canonical correlation, etc. It is important to assess multivariate normality in order to proceed with such statistical methods. There are many analytical methods proposed for checking multivariate normality. However, deciding which method to use is a challenging process, since each method may give different results under certain conditions. Hence, we may say that there is no best method, which is valid under any condition, for normality checking. In addition to numerical results, it is very useful to use graphical methods to decide on multivariate normality. Combining the numerical results from several methods with graphical approaches can be useful and provide more reliable decisions. Here, we present an R package, MVN, to assess multivariate normality. It contains the three most widely used multivariate normality tests, including Mardia's, Henze-Zirkler's and Royston's, and graphical approaches, including chi-square Q-Q, perspective and contour plots. It also includes two multivariate outlier detection methods, which are based on robust Mahalanobis distances. Moreover, this package offers functions to check the univariate normality of marginal distributions through both tests and plots. Furthermore, especially for non-R users, we provide a user-friendly web application of the package. This application is available at http://www.biosoft.hacettepe.edu.tr/MVN/.

/pdf/mvn-an-r-package-for-assessing-multivariate-normality-49478mtulc.pdf

MVN: An R Package for Assessing Multivariate Normality

Energy statistics: A class of statistics based on distances

Linear algebra.- Random vectors.- Gamma, Dirichlet, and F distributions.- Invariance.- Multivariate normal.- Multivariate sampling.- Wishart distributions.- Tests on mean and variance.- Multivariate regression.- Principal components.- Canonical correlations.- Asymptotic expansions.- Robustness.- Bootstrap confidence regions and tests.

/pdf/theory-of-multivariate-statistics-4zygvrlfbu.pdf

Theory of multivariate statistics

A new test for multivariate normality

https://www.econstor.eu/bitstream/10419/50931/1/349052875.pdf

Contribution to Productivity or Pork Barrel? : The Two Faces of Infrastructure Investment

Let be independent identically distributed random vectors in Rd d ≥ 1 , with sample mean [Xbar] n and sample covariance matrix S n . We present a class of practicable afflne-invariant tests for the composite hypothesis H d the law of X 1 is a non-degenerate normal distribution which are consistent against any fixed non- normal alternative distribution. The test statistic is a weighted integral of the squared modulus of the difference between the empirical characteristic function of the scaled residuals and its pointwise limit under H d - An alternative representation is given in terms of an L 2-distance between densities. The limiting null distribution of the test statistic is obtained. Power performance of the new tests is assessed in a Monte Carlo study.

B. Zirkler

Papers

A class of invariant consistent tests for multivariate normality