Własności testów wielowymiarowej normalności opartych na miarach kształtu

Abstract

The assumption of multivariate normality is the basis of the standard methodology of multivariate mathematical statistics. The commonness of the use of the multivariate normal distribution is mainly implied by properties of this distribution in comparison with other multivariate distributions. Investigating the influence of the departures from normality on the used methods of constructing confidence intervals and diverse testing procedures is neither easy nor successfully implemented. Statistical methods to analyze multivariate numerical data robust to departures from normality are still at their early stage of development. It is of great use to have procedures for testing reasonable assumptions of multivariate normality for a given set of observed random vectors, especially for the ones from laboratory testing designs or time series. There are many tests of multivariate normality. Their number follows from their usefulness to investigate different departures from multivariate normality. In the article the results concerning the power of tests based on the measures of shape, derived from both analytical and Monte Carlo investigations, are presented. The multivariate coefficients of the measures of shape are also applied as statistics characterizing multivariate sample. That is why the research of the tests of multivariate normality based on the measures of skewness and kurtosis was carried out.