Estimating common standard deviation of two normal populations with ordered means

Manas Tripathy (), Somesh Kumar () and Nabendu Pal ()

Statistical Methods & Applications, 2013, vol. 22, issue 3, 305-318

Abstract: 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. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Admissible estimator; Equivariant estimator; Maximum likelihood estimator; Minimax estimator; Ordered parameters.; 62F10; 62C20 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10260-012-0224-1

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