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

Ouimet, Frédéric (2022) Local Normal Approximations and Probability Metric Bounds for the Matrix-Variate T Distribution and Its Application to Hotelling’s T Statistic. AppliedMath, 2 (3). pp. 446-456. ISSN 2673-9909. doi:10.3390/appliedmath2030025. https://resolver.caltech.edu/CaltechAUTHORS:20220802-730840000

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.3390/appliedmath2030025DOIArticle
https://arxiv.org/abs/2202.04100arXivDiscussion Paper
ORCID:
AuthorORCID
Ouimet, Frédéric0000-0001-7933-5265
Additional Information:© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Received: 22 June 2022 / Revised: 18 July 2022 / Accepted: 21 July 2022 / Published: 1 August 2022. We thank the three referees for their comments. F.O. is supported by postdoctoral fellowships from the NSERC (PDF) and the FRQNT (B3X supplement and B3XR). Data Availability Statement. The R code for the simulations in Section 2 is in Supplementary Material. The author declares no conflict of interest. Institutional Review Board Statement. Not applicable. Informed Consent Statement. Not applicable.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Fonds de recherche du Québec - Nature et technologies (FRQNT)B3X
Fonds de recherche du Québec – Nature et technologies (FRQNT)B3XR
Subject Keywords: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
Issue or Number:3
DOI:10.3390/appliedmath2030025
Record Number:CaltechAUTHORS:20220802-730840000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220802-730840000
Official Citation:Ouimet, Frédéric. 2022. "Local Normal Approximations and Probability Metric Bounds for the Matrix-Variate T Distribution and Its Application to Hotelling’s T Statistic" AppliedMath 2, no. 3: 446-456. https://doi.org/10.3390/appliedmath2030025
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116041
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:02 Aug 2022 16:20
Last Modified:02 Aug 2022 16:20

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