Electronic Journal of Statistics

Shrinkage estimation with a matrix loss function

Reman Abu-Shanab, John T. Kent, and William E. Strawderman

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Consider estimating an $n\times p$ matrix of means $\Theta$, say, from an $n\times p$ matrix of observations $X$, where the elements of $X$ are assumed to be independently normally distributed with $E(x_{ij})=\theta_{ij}$ and constant variance, and where the performance of an estimator is judged using a $p\times p$ 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 $n\geq 3$. This result also extends to other shrinkage estimators and settings.

Article information

Electron. J. Statist., Volume 6 (2012), 2347-2355.

First available in Project Euclid: 14 December 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C99: None of the above, but in this section
Secondary: 62H12: Estimation

James-Stein estimator matrix quadratic loss function risk Stein’s Lemma


Abu-Shanab, Reman; Kent, John T.; Strawderman, William E. Shrinkage estimation with a matrix loss function. Electron. J. Statist. 6 (2012), 2347--2355. doi:10.1214/12-EJS748. https://projecteuclid.org/euclid.ejs/1355495988

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