Estimating common standard deviation of two normal populations with ordered means

摘要

Independent random samples are taken from two normal populations with means (mu _1) and (mu _2) and a common unknown variance (sigma ^2.) It is known that (mu _1le mu _2.) In this paper, estimation of the common standard deviation (sigma ) is considered with respect to a scale invariant loss function. A general minimaxity result is proved and a class of minimax estimators is derived. An admissibility result is proved in this class. Further a class of equivariant estimators with respect to a subgroup of affine group is considered and dominating estimators in this class are obtained. The risk performance of some of these estimators is compared numerically.