IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v52y2001i1p9-19.html
   My bibliography  Save this article

Estimating quantiles of a selected exponential population

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(00)00174-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kumar, Somesh & Sharma, Divakar, 1996. "A note on estimating quantiles of exponential populations," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 115-118, February.
    2. 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.
    3. Sharma Divakar & Kumar Somesh, 1994. "Estimating Quantiles Of Exponential Populations," Statistics & Risk Modeling, De Gruyter, vol. 12(4), pages 343-352, April.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Deshpande, Jayant V. & Muhammad Fareed, T. P., 1995. "A note on conditionally unbiased estimation after selection," Statistics & Probability Letters, Elsevier, vol. 22(1), pages 17-23, January.
    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. 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.
    5. Sill, Michael W. & Sampson, Allan R., 2009. "Drop-the-losers design: Binomial case," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 586-595, January.
    6. Nigel Stallard & Peter K Kimani, 2018. "Uniformly minimum variance conditionally unbiased estimation in multi-arm multi-stage clinical trials," Biometrika, Biometrika Trust, vol. 105(2), pages 495-501.
    7. Vellaisamy, P. & Jain, Sushmita, 2008. "Estimating the parameter of the population selected from discrete exponential family," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1076-1087, July.
    8. Haibing Zhao & Xinping Cui, 2020. "Constructing confidence intervals for selected parameters," Biometrics, The International Biometric Society, vol. 76(4), pages 1098-1108, December.
    9. Per Broberg & Frank Miller, 2017. "Conditional estimation in two-stage adaptive designs," Biometrics, The International Biometric Society, vol. 73(3), pages 895-904, September.
    10. Rosenkranz, Gerd K., 2014. "Bootstrap corrections of treatment effect estimates following selection," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 220-227.
    11. P. Vellaisamy & Abraham Punnen, 2002. "Improved estimators for the selected location parameters," Statistical Papers, Springer, vol. 43(2), pages 291-299, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:52:y:2001:i:1:p:9-19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.