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Estimating quantiles of a selected exponential population

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  • Kumar, Somesh
  • Kar, Aditi

Abstract

Suppose independent random samples are available from k exponential populations with a common location [theta] and scale parameters [sigma]1,[sigma]2,...,[sigma]k, respectively. The population corresponding to the largest sample mean is selected. The problem is to estimate a quantile of the selected population. In this paper, we derive the uniformly minimum variance unbiased estimator (UMVUE) using (U-V) method of Robbins (in: Gupta and Berger (Eds.), Statistical Decision Theory and Related Topics -- IV, Vol. 1, Springer, New York, 1987, pp. 265-270) and Rao-Blackwellization. Further, a general inadmissibility result for affine equivariant estimators is proved. As a consequence, an estimator improving upon the UMVUE with respect to the squared error and the scale invariant loss functions is obtained.

Suggested Citation

  • Kumar, Somesh & Kar, Aditi, 2001. "Estimating quantiles of a selected exponential population," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 9-19, March.
    • Handle: RePEc:eee:stapro:v:52:y:2001:i:1:p:9-19
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    References listed on IDEAS

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    1. P. Vellaisamy, 1992. "Average worth and simultaneous estimation of the selected subset," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 551-562, September.
    2. Sharma Divakar & Kumar Somesh, 1994. "Estimating Quantiles Of Exponential Populations," Statistics & Risk Modeling, De Gruyter, vol. 12(4), pages 343-352, April.
    3. Kumar, Somesh & Sharma, Divakar, 1996. "A note on estimating quantiles of exponential populations," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 115-118, February.
    4. Cohen, Arthur & Sackrowitz, Harold B., 1989. "Two stage conditionally unbiased estimators of the selected mean," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 273-278, August.
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    Cited by:

    1. Morteza Amini & Nader Nematollahi, 2017. "Estimation of the Parameters of a Selected Multivariate Population," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 13-38, February.
    2. Riyadh Al-mosawi, 2012. "Simultaneous estimation following subset selection of binomial populations," METRON, Springer;Sapienza Università di Roma, vol. 70(1), pages 59-69, April.
    3. Kumar, Somesh & Mahapatra, Ajaya Kumar & Vellaisamy, P., 2009. "Reliability estimation of the selected exponential populations," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1372-1377, June.

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