Accession Number : ADA332223

Title :   An Overall Test for Multivariate Normality.

Descriptive Note : Technical rept.,

Corporate Author : PENNSYLVANIA STATE UNIV UNIVERSITY PARK CENTER FOR MULTIVARIATE ANALYSIS

Personal Author(s) : Rao, C. R. ; Ali, Hydar

PDF Url : ADA332223

Report Date : SEP 1997

Pagination or Media Count : 9

Abstract : There are a number of methods in the statistical literature for testing whether observed data came from a multivariate normal(MVN) distribution with an unknown mean vector and covariance matrix. Let X1, ... be an iid sample of size n from a p-variate normal distribution. Denote the sample mean and sample variance-covariance matrix by X and S respectively. Most of the tests of multivariate normality are based on the results that Yi-S-1/2(Xi - X), i=1,.., n, are asymptotically iid as p-variate normal than zero mean vector and identity covariance matrix. Tests developed by Andrews et al., Mardina and others are direct functions of Yi. We note that the N=np components of the Yi's put together can be considered as an asymptotically iid sample of size N from a univariate normal any well known test based on N independent observations for univariate normality. In Particular we can use univariate skewness and kurtosis tests, which are sensitive to deviations from normality.

Descriptors :   *MULTIVARIATE ANALYSIS, MATRICES(MATHEMATICS), STATISTICS, SENSITIVITY, VARIATIONS, COVARIANCE, STATISTICAL DISTRIBUTIONS, SKEWNESS, FUNCTIONS(MATHEMATICS), NORMALITY.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE