On a shrinkage estimator of a normal common mean vector

Abstract

The problem of estimating the p × 1 mean vector θ based on two independent normal vectors Y 1 ∼ N p ( θ, σ 2 I) and Y 2 ∼ N p ( θ, ξσ 2 I) is considered. For p ≥ 3, when ξ and σ 2 are unknown, it was shown by George (1991, Ann. Statist.) that under certain conditions estimators of the form δ η = ηY 1 + (1 − η) Y 2, where η is a fixed number in (0, 1), are uniformly dominated by a shrinkage estimator under the squared error loss. In this paper, George's result is improved by obtaining a simpler and better condition for the domination.