Estimating common standard deviation of two normal populations with ordered means
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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 \(\mu _1\le \mu _2.\) 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.
KeywordsAdmissible estimator Equivariant estimator Maximum likelihood estimator Minimax estimator Ordered parameters.
Mathematics Subject Classification (2000)62F10 62C20
The authors thank the reviewers and the Editor-in-Chief for their suggestions which have considerably improved the paper.
- Tripathy MR, Kumar S (2011) Simultaneous estimation of quantiles of normal populations with ordered means. J Combin Inform Syst Sci 36(1):75–102Google Scholar