Shrinkage estimation with a matrix loss function

Details Shrinkage estimation with a matrix loss function Shrinkage estimation with a matrix loss function

2011-01-18

arxiv.org/abs/1101.3412v1

Mathematics

Statistics Theory

8 pages

Scientific paper

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.

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