Improved loss estimation for a normal mean matrix

Takeru Matsuda and William E. Strawderman

Journal of Multivariate Analysis, 2019, vol. 169, issue C, 300-311

Abstract: 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.

Keywords: Loss estimation; Matrix mean; Reduced-rank regression; Shrinkage estimator; Singular value decomposition (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.jmva.2018.10.001

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