An Overall Test for Multivariate Normality.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1997
- Accession Number
- ADA332223
Entities
People
- Calyampudi Radhakrishna Rao
- Hydar Ali
Organizations
- Pennsylvania State University