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Empirical Bayes on vector observations: An extension of Stein's method

1972; Oxford University Press; Volume: 59; Issue: 2 Linguagem: Inglês

10.1093/biomet/59.2.335

1464-3510

Bradley Efron, Carl N. Morris,

Advanced Statistical Methods and Models

The statistician is considering several independent normal linear models with identical structures, and desires to estimate the vector of unknown parameters in each of them. An estimator is constructed which dominates the usual Gauss-Markov estimator in terms of total squared error loss. This estimator is shown to have good efficiency in the Bayesian situation where the parameter vectors themselves have a normal prior distribution. A practical example is given.