## Shrinkage estimation with a matrix loss functionReman Abu-Shanab, John T. Kent and William E. Strawderman Consider estimating the n by p matrix of means of an n by p matrix of independent normally distributed observations with constant variance, where the performance of an estimator is judged using a p by p matrix quadratic error loss function. A matrix version of the James-Stein estimator is proposed, depending on a tuning constant. It is shown to dominate the usual maximum likelihood estimator for some choices of of the tuning constant when n is greater than or equal to 3. This result also extends to other shrinkage estimators and settings. Key words: cross-product inequality, James-Stein estimation, multivariate normal distribution, squared error loss Back |