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Simultaneous estimation following subset selection of binomial populations

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  • Riyadh Al-mosawi

Abstract

Let π 1 , …, π p be p (p ≥2) independent populations with π i being binomial bin(l, θ) with an unknown parameter θ i i=1, …, p. Suppose independent random samples of sizes n 1 , …, n p are drawn from the populations π 1 , …, π p , respectively, and let $${erline X}_i=X_i/n_i$$, where $$X_{i}={Sigma^{ni}_{j=1}}X_{ij},i=1,$$ …, P. We call the population associated with the largest of θ i ’s the best population. Suppose a population is selected using the Gupta’s (Gupta, S. S. (1965). On some multiple decision(selection and ranking) rules. Technometrics 7, 225–245) subset selection procedure. In this paper, we consider simultaneous estimation of the parameters of the selected populations. It is shown that neither the unbiased estimator nor the riskunbiased estimator (corresponding to the normalized squared error loss function) exists based on a single-stage sample. When additional observations are available from the selected populations, we derive an unbiased and risk-unbiased estimators for the selected subset and also prove that the natural estimators are positively biased. Finally, the bias and the risk of the natural, unbiased and risk-unbiased estimators are computed using Monte-Carlo simulation method. Copyright Sapienza Università di Roma 2012

Suggested Citation

  • 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.
  • Handle: RePEc:spr:metron:v:70:y:2012:i:1:p:59-69
    DOI: 10.1007/BF03263571
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    References listed on IDEAS

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    1. Kumar, Somesh & Kar, Aditi, 2001. "Estimating quantiles of a selected exponential population," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 9-19, March.
    2. Neeraj Misra & Edward Meulen, 2003. "On estimating the mean of the selected normal population under the LINEX loss function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 173-183, September.
    3. 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.
    4. 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.
    5. 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.
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