Improved loss estimation for a normal mean matrix
type: Item
instance of: scholarly article
title: Improved loss estimation for a normal mean matrix
zbMATH Open document ID: 1414.62185
author: T. Matsuda
author: William E. Strawderman
published in: Journal of Multivariate Analysis
publication date: 2019-01-04T00:00:00Z
review text: For an \((n,m)\)-matrix \(X(\omega)\) composed of independent, normal distributed elements \(X_{ij}\) with mean \(M_{ij}\) and variance \(1\), consider estimates \(\hat{M}=\hat{M}(X)\) of the mean matrix \(M\), given an observation \(X\) of \(X(\omega)\). An estimator \(\hat{M}\) is evaluated by the estimation error \(L(X)=\|\hat{M}(X) - M\|^2\) with the Euclidean matrix norm \(\| \cdot \|^2\). The performance of a loss estimator \(\lambda(X)\) is defined by its mean square deviation \({E_M}(\lambda(X) - L(X))^2\) from \(L(X)\), given the mean matrix \(M\). Loss estimators are constructed which dominate the unique unbiased loss estimator (according to [\textit{C. Stein}, Proc. Prague Symp. Asympt. Stat., Vol. II, Prague 1973, 345--381 (1974; Zbl 0357.62020)]) for a large class of matrix mean estimators. For illustration of the results, numerical experiments are presented.
reviewed by: Kurt Marti
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62J07
zbMATH DE Number: 6997759
zbMATH Keywords: loss estimation
zbMATH Keywords: matrix mean estimation
zbMATH Keywords: reduced-rank regression
zbMATH Keywords: shrinkage estimator
zbMATH Keywords: singular value decomposition
MaRDI profile type: Publication
full work available at URL: j.jmva.2018.10.001
OpenAlex ID: W2897264040
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Wikidata QID: Q129115088
DOI: 10.1016/J.JMVA.2018.10.001
description: scientific article; zbMATH DE number 6997759