Matrix quadratic risk of orthogonally invariant estimators for a normal mean matrix-Reference-Cited by-同舟云学术

Matrix quadratic risk of orthogonally invariant estimators for a normal mean matrix

Published:2023-08-22 Issue: Volume: Page:
ISSN:2520-8756
Container-title:Japanese Journal of Statistics and Data Science
language:en
Short-container-title:Jpn J Stat Data Sci

Author:

Matsuda Takeru^ORCID

Abstract

AbstractIn estimation of a normal mean matrix under the matrix quadratic loss, we develop a general formula for the matrix quadratic risk of orthogonally invariant estimators. The derivation is based on several formulas for matrix derivatives of orthogonally invariant functions of matrices. As an application, we calculate the matrix quadratic risk of a singular value shrinkage estimator motivated by Stein’s proposal for improving on the Efron–Morris estimator 50 years ago.

Funder

Japan Society for the Promotion of Science London

Japan Science and Technology Corporation

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Statistics and Probability

Link

https://link.springer.com/content/pdf/10.1007/s42081-023-00216-z.pdf

Reference11 articles.

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4. Matsuda, T., & Komaki, F. (2015). Singular value shrinkage priors for Bayesian prediction. Biometrika, 102, 843–854.

5. Matsuda, T., & Strawderman, W. E. (2022). Estimation under matrix quadratic loss and matrix superharmonicity. Biometrika, 109, 503–519.

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