THE EXPECTED VALUES OF INVARIANT POLYNOMIALS WITH MATRIX ARGUMENT OF ELLIPTICAL DISTRIBUTIONS

Invariant polynomials with matrix arguments have been defined by the theory of group representation, generalizing the zonal polynomials. They have developed as a useful tool to evaluate certain integrals arising in multivariate distribution theory, which were expanded as power series in terms of the invariant polynomials. Some interesting polynomials has been shown by people working in the field of econometric theory. In this paper. we derive the expected values of C (BR.BU). Ck (BR)C (BU) and Ck (B-1U), where Bd＝X′X and Xnxp is distributed according to an elliptical matrix distribution. We also give their applications in multivariate distribution theory including the related development in econometrics.

Some Comments on Zonal Polynomials and Their Expected Values with respect to Elliptical.Distributions

In this paper, we give alternative proofs of some results in [15] （Li R.,1997） about the expected value of zonal polynomials.

微分环上矩阵变元的带状多项式及应用

本文对称数阵为变元的带状多项式进一步推广，给出了微分环上矩阵变元的带状多项式的一些性质，并且把它应用于对第一和第二类非中心椭球等高分布的研究。

广义双非中心F分布和β分布

给出了在修正的第二类椭球等高分布下的双非中心Ｆ分布和β分布，这些结果同样可以推广到第一类椭球等高分布下．

椭球等高分布族下随机矩阵商的特征根分布

在椭球等高分布族情形下,讨论广义非中心Wishart短阵商的特征根精确分布问题,并给出了一般情形下广义非中心F统计量的特征根精确分布。