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Estimating common standard deviation of two normal populations with ordered means

Author

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  • Manas Tripathy
  • Somesh Kumar
  • Nabendu Pal

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

Suggested Citation

  • Manas Tripathy & Somesh Kumar & Nabendu Pal, 2013. "Estimating common standard deviation of two normal populations with ordered means," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 305-318, August.
    • Handle: RePEc:spr:stmapp:v:22:y:2013:i:3:p:305-318
    DOI: 10.1007/s10260-012-0224-1
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    Citations

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    Cited by:

    1. Pravash Jena & Manas Ranjan Tripathy & Somesh Kumar, 2023. "Point and Interval Estimation of Powers of Scale Parameters for Two Normal Populations with a Common Mean," Statistical Papers, Springer, vol. 64(5), pages 1775-1804, October.
    2. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2021. "Minimax estimation of the common variance and precision of two normal populations with ordered restricted means," Statistical Papers, Springer, vol. 62(1), pages 209-233, February.

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