Local normal approximations and probability metric bounds for the matrix-variate $T$ distribution and its application to Hotelling's $T$ statistic
Statistics Theory
2022-11-18 v2 Probability
Statistics Theory
Abstract
In this paper, we develop local expansions for the ratio of the centered matrix-variate 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 of the results of Shafiei & Saberali (2015) and Ouimet (2022) for the univariate Student distribution to the matrix-variate setting.
Keywords
Cite
@article{arxiv.2202.04100,
title = {Local normal approximations and probability metric bounds for the matrix-variate $T$ distribution and its application to Hotelling's $T$ statistic},
author = {Frédéric Ouimet},
journal= {arXiv preprint arXiv:2202.04100},
year = {2022}
}
Comments
11 pages, 2 figures