Estimation of a Normal Mean Vector Under Known Scale

This chapter is devoted to estimation of a normal mean vector when the covariance matrix is a known multiple of the identity matrix, (i.e., the known scale case) and the loss is scaled squared error. The focus is on admissibility, inadmissibility and minimaxity of (generalized) Bayes estimators. Particular attention is paid to the class of (generalized) Bayes estimators with respect to an extended Strawderman-type prior. We also consider improvements on the James–Stein estimator. The proofs are self-contained.