## Electronic Journal of Statistics

### Shrinkage estimation with a matrix loss function

#### Abstract

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

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

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1355495988

Digital Object Identifier
doi:10.1214/12-EJS748

Mathematical Reviews number (MathSciNet)
MR3020266

Zentralblatt MATH identifier
1295.62070

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

#### Citation

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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