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Statistical Methods & Applications

, Volume 22, Issue 3, pp 305–318 | Cite as

Estimating common standard deviation of two normal populations with ordered means

  • Manas Ranjan Tripathy
  • Somesh KumarEmail author
  • Nabendu Pal
Article

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.

Keywords

Admissible estimator Equivariant estimator Maximum likelihood estimator Minimax estimator Ordered parameters. 

Mathematics Subject Classification (2000)

62F10 62C20 

Notes

Acknowledgments

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Manas Ranjan Tripathy
    • 1
  • Somesh Kumar
    • 2
    Email author
  • Nabendu Pal
    • 3
  1. 1.Department of MathematicsNational Institute of TechnologyRourkelaIndia
  2. 2.Department of MathematicsIndian Institute of TechnologyKharagpurIndia
  3. 3.Department of MathematicsUniversity of Louisiana at LafayetteLafayetteUSA

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