Shrinkage estimation with a matrix loss function
Statistics Theory
2011-01-19 v1 Statistics Theory
Abstract
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.
Cite
@article{arxiv.1101.3412,
title = {Shrinkage estimation with a matrix loss function},
author = {Reman Abu-Shanab and John T. Kent and William E. Strawderman},
journal= {arXiv preprint arXiv:1101.3412},
year = {2011}
}
Comments
8 pages