ESTIMATION OF A COMMON MULTIVARIATE NORMAL MEAN VECTOR

K. KRISHNAMOORTHY

Department of Statistics, Temple University, Philadelphia, PA 19122, U.S.A.

(Received December 4, 1989; revised June 6, 1990)

Abstract. Let X_{1}, …, X_{N} be independent observations from N_{p}(μ, Σ_{1}) and Y_{1}, …, Y_{N} be independent observations from N_{p}(μ, Σ_{2}). Assume that X_{i}’s and Y_{i}’s are independent. An unbiased estimator of μ which dominates the sample mean X̄ for p ≥ 1 under the loss function L(μ, μ̂) = (μ̂ − μ)′Σ_{1}^{−1}(μ̂ − μ) is suggested. The exact risk (under L) of the new estimator is also evaluated.

Key words and phrases: Common mean vector, unbiased estimator, Wishart and noncentral Wishart distributions.