(Received August 20, 1990; revised February 20, 1991)
Abstract. Asymptotic risk behavior of estimators of the unknown variance and of the unknown mean vector in a multivariate normal distribution is considered for a general loss. It is shown that in both problems this characteristic is related to the risk in an estimation problem of a positive normal mean under quadratic loss function. A curious property of the Brewster-Zidek variance estimator of the normal variance is also noticed.
Key words and phrases: Bowl-shaped loss function, Brewster-Zidek estimator of normal variance, James-Stein estimator of normal mean, relative risk reduction, positive normal mean, Stein estimator of normal variance.
Source ( TeX , DVI , PS )