Estimating the Mean of a Normal Distribution with Known Coefficient of Variation

Abstract

Estimation of the mean θ of a normal distribution N (θ, aθ 2 ) with known coefficient of variation a 1/2 is treated as a decision problem with squared-error loss. It is shown that all estimators linear in the sample mean and sample standard deviation s , as well as the maximum likelihood estimator (MLE), are dominated in risk by the admissible, minimum risk, scale equivariant estimator . A class of Bayes estimators against inverted-gamma priors is constructed, and shown to include within its closure. All members of this latter class, as well as , can be easily computed using continued fractions.