Maximization of an Integral of a Matrix Function and Asymptotic Expansions of Distributions of Latent Roots of Two Matrices
矩阵函数积分的极大化及两个矩阵特征根分布的渐近展开
The noncentral distribution of latent roots arising in several situations in multivariate analysis involves the integration of a hypergeometric function of matrix variates over a group of orthogonal matrices in the real case and that of unitary matrices in the complex case. In this paper the subgroup of the orthogonal group (unitary group) for which the integrand is maximized has been found under mild restrictions. The results of earlier authors (Anderson, Chang, James, Li…