Comparisons of the Performances of Estimators of a Bounded Normal Mean Under Squared-Error Loss

Abstract

This paper is concerned with the estimation under squared-error loss of a normal mean θ based on X ∼ N (θ, 1) when |θ| ≤ m for a known m > 0. Nine estimators are compared, namely the maximum likelihood estimator (mle), three dominators of the mle obtained from Moors, from Charras and from Charras and van Eeden, two minimax estimators from Casella and Strawderman, a Bayes estimator of Marchand and Perron, the Pitman estimator and Bickel’s asymptotically-minimax estimator. The comparisons are based on analytical as well as on graphical results concerning their risk functions. In particular, we comment on their gain in accuracy from using the restriction, as well as on their robustness with respect to misspecification of m.