Asymtotic expansions of the null distribution of test statistics for multivariate linear hypothesis under nonnormality

摘要

This paper is concerned with the distributions of some test statistics for a multivariate linear hypothesis under nonnormality. The test statistics considered in- clude the likelihood ratio statistic, the Lawley-Hotelling trace criterion and the Bartlett- Nanda-Pillai trace criterion, under normality. We derive asymptotic expansions of the Null distributions of these test statistics up to the order n~-1, where n is the sample size, Under nonnormality. It is shown that our general results can be effectively obtained by Deriving an asymptotic expansion of the distribution of a multivariate t-statistic.