Shrinkage estimation with a matrix loss function

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Abstract

Consider estimating an n×p matrix of means Θ, say, from an n×p matrix of observations X, where the elements of X are assumed to be independently normally distributed with E(xij)=θij and constant variance, and where the performance of an estimator is judged using a p×p matrix quadratic error loss function. A matrix version of the James-Stein estimator is proposed, depending on a tuning constant a. It is shown to dominate the usual maximum likelihood estimator for some choices of a when n≥3. This result also extends to other shrinkage estimators and settings.

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APA

Abu-Shanab, R., Kent, J. T., & Strawderman, W. E. (2012). Shrinkage estimation with a matrix loss function. Electronic Journal of Statistics, 6, 2347–2355. https://doi.org/10.1214/12-EJS748

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