On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices

被引：1

作者：

Genest, C. ^{[1
]}

Ouimet, F. ^{[1
]}

Richards, D. ^{[2
]}

机构：

[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada

[2] Penn State Univ, Dept Stat, University Pk, PA USA

来源：

STAT | 2024年 / 13卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Gaussian product inequality; moments; principal minors; Schur complement; Wishart distribution; zonal polynomials; PRODUCTS;

D O I：

10.1002/sta4.706

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of sample statistics in various applications related to multivariate linear regression. These important but little-known moment results were extended in 1963 by the Australian statistician A. Graham Constantine using Bartlett's decomposition. In this note, a new proof of Wilks' results is derived using the concept of iterated Schur complements, thereby bypassing Bartlett's decomposition. Furthermore, Wilks' open problem of evaluating joint moments of disjoint principal minors of Wishart random matrices is related to the Gaussian product inequality conjecture.

引用

页数：6

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