ESTIMATION OF A COMMON MULTIVARIATE NORMAL MEAN VECTOR

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 X₁,...., X_N be independent observations from N_p(mu, Sigma₁) and Y₁,...., Y_N be independent observations from N_p(mu, Sigma₂). Assume that X_i's and Y_i's are independent. An unbiased estimator of mu which dominates the sample mean \bar X for p > 1 under the loss function L(mu, ^{^}mu) = (^{^}mu - mu)'Sigma₁^-1(^{^}mu-mu) 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.

Source ( TeX , DVI , PS )