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Estimation of the Parameters of a Selected Multivariate Population

Author

Listed:
  • Morteza Amini

    (University of Tehran)

  • Nader Nematollahi

    (Allameh Tabataba’i University)

Abstract

The problem of estimation of the parameters of a selected univariate distribution has been studied extensively in the literature, in which a one dimensional random parameter is estimated using a random sample of one dimensional observations. There are situations where the selection process is performed using multiple variables or the selection of the population is done using an auxiliary variable. It is natural that such a random vector has a multivariate distribution with a multidimensional parameter space. In this paper, certain methods are developed for estimation of the multidimensional parameters of the selected multivariate distribution. The risks of the proposed estimators are estimated and certain sufficient conditions for inadmissibility of the estimators are given for two classes of the estimators. The results are applied to a prostate cancer data set to illustrate the applicability of theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:79:y:2017:i:1:d:10.1007_s13171-016-0093-z
    DOI: 10.1007/s13171-016-0093-z
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    References listed on IDEAS

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    1. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    2. 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.
    3. Kumar, Somesh & Kar, Aditi, 2001. "Estimating quantiles of a selected exponential population," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 9-19, March.
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