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

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 dist...

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Bibliographic Details
Published in:AppliedMath 2022-08, Vol.2 (3), p.446-456
Main Author: Ouimet, Frédéric
Format: Article
Language:English
Subjects:
asymptotic statistics
expansion
Hotelling’s T statistic
Hotelling’s T-squared statistic
local approximation
matrix-variate normal distribution
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Summary: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.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath2030025