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 of the results of Shafiei & Saberali (2015) and Ouimet (2022) for the univariate Student distribution to the matrix-variate setting.

翻译：在本文中,我们开发了以中矩阵变差($T)密度为核心矩阵变差($T)密度与中矩阵变差($T)正常密度之比的本地扩展。近似值用于根据相应引因措施之间的数种概率度量(如总变差和海灵格距离)得出上限。这项工作将Shafiei & Saberali(2015年)和Ouimet(2022年)的一些结果延伸至单象形变差学生分布到矩阵变差设置。