Estimating the Mean of a Normal Distribution with Known Coefficient of Variation
已知变异系数时正态分布均值的估计
Estimation of the mean θ of a normal distribution N(θ, aθ2) 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…