Local Normal Approximations and Probability Metric Bounds for the Matrix-Variate T Distribution and Its Application to Hotelling's T Statistic

被引：0
|
作者：
Ouimet, Frederic [1 ,2 ]
机构：
[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada
[2] CALTECH, Div Phys Math & Astron, Pasadena, CA 91125 USA
来源：
APPLIEDMATH | 2022年 / 2卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
asymptotic statistics; expansion; Hotelling's T-squared statistic; Hotelling's T statistic; matrix-variate normal distribution; local approximation; matrix-variate T distribution; normal approximation; Student distribution; T distribution; total variation; DIFFUSION; EIGENVALUES; MOMENTS; DESIGN; MRI;
D O I：
10.3390/appliedmath2030025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop local expansions for the ratio of the centered matrix-variate T density to the centered matrix-variate normal density with the same covariances. The approximations are used to derive upper bounds on several probability metrics (such as the total variation and Hellinger distance) between the corresponding induced measures. This work extends some previous results for the univariate Student distribution to the matrix-variate setting.
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页码：446 / 456
页数：11
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