Published August 2, 2022
| Supplemental Material + Published + Accepted Version
Journal Article
Open
Local Normal Approximations and Probability Metric Bounds for the Matrix-Variate T Distribution and Its Application to Hotelling's T Statistic
- Creators
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Ouimet, Frédéric
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.
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.Attached Files
Published - appliedmath-02-00025.pdf
Accepted Version - 2202.04100.pdf
Supplemental Material - appliedmath-02-00025-s001.zip
Files
appliedmath-02-00025-s001.zip
Additional details
- Eprint ID
- 116041
- Resolver ID
- CaltechAUTHORS:20220802-730840000
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- B3X
- Fonds de recherche du Québec - Nature et technologies (FRQNT)
- B3XR
- Fonds de recherche du Québec – Nature et technologies (FRQNT)
- Created
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2022-08-02Created from EPrint's datestamp field
- Updated
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2022-08-02Created from EPrint's last_modified field