Abstract
This is a continuation of the survey paper [38] by the present author. In this Part II, the following methods are reviewed: (3) method based on the system of partial differential equations satisfied by the hypergeometric functions, (4) method by an expansion of test statistics in terms of normal variates, and (5) method based on the representation of an orthogonal matrix by a skew symmetric matrix. Finally some comments are given on what kinds of statistical works are to be done in future based on the asymptotic expansions obtained by the methods explained in this paper.
