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Estimating common standard deviation of two normal populations with ordered means

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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.

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Acknowledgments

The authors thank the reviewers and the Editor-in-Chief for their suggestions which have considerably improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Rourkela, 769008, India

    Manas Ranjan Tripathy

  2. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India

    Somesh Kumar

  3. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA

    Nabendu Pal

Authors
  1. Manas Ranjan Tripathy
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  2. Somesh Kumar
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  3. Nabendu Pal
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Correspondence to Somesh Kumar.

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Tripathy, M.R., Kumar, S. & Pal, N. Estimating common standard deviation of two normal populations with ordered means. Stat Methods Appl 22, 305–318 (2013). https://doi.org/10.1007/s10260-012-0224-1

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  • DOI: https://doi.org/10.1007/s10260-012-0224-1

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