Asymptotic expansion for sampling distribution and sample size in statistical inference I-Presentation of the problem, illustrated by the T2-test

Inference procedures in the multivariate analysis are often based on asymptotic expansions for the distributions of statistics under consideration. The precision of asymptotic expansion formula depends on dimensionality, sample size and noncentrality parameter. The aim of this research is to search an effective method applicable for the general problem in the title. In order to illustrate the problem concretely, the asymptotic expansion formula for the operating characteristic function of Hotelling’s T²-test was considered and showed how to obtain an experimental formula giving an approximate upper bound to the absolute error of the formula. It was discussed how to determine an effective sample size satisfying a requirement on the absolute error based on the experimental formula thus obtained.