Improved loss estimation for a normal mean matrix

JOURNAL OF MULTIVARIATE ANALYSIS

卷:169

Article

Matsuda, Takeru¹  Strawderman, William E.² 

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Tokyo, Japan

[2] Rutgers State Univ, Dept Stat & Biostat, New Brunswick, NJ USA

关键词: Loss estimation;    Matrix mean;    Reduced-rank regression;    Shrinkage estimator;    Singular value decomposition;   

DOI  :  10.1016/j.jmva.2018.10.001

来源: Elsevier

【 摘 要 】

We investigate improved loss estimation in the matrix mean estimation problem. Specifically, for estimators of a normal mean matrix, we consider estimation of the Frobenius loss. Based on the singular values of the observation, we develop loss estimators that dominate the unbiased loss estimator for a broad class of matrix mean estimators including the Efron-Morris estimator. This is an extension of the results of Johnstone (1988) for a normal mean vector. We also provide improved estimators of loss for reduced-rank estimators. Numerical results show the effectiveness of the proposed loss estimators. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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