Simultaneous estimation of Poisson means of the selected subset |
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Authors: | P. Vellaisamy Riyadh Al-Mosawi |
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Affiliation: | 1. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India;2. Department of Mathematics, Thiqar University, Thiqar, Iraq |
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Abstract: | Let π1,π2,…,πp be p independent Poisson populations with means λ1,…,λp, respectively. Let {X1,…,Xp} denote the set of observations, where Xi is from πi. Suppose a subset of populations is selected using Gupta and Huang's (1975) selection rule which selects πi if and only if Xi+1?cX(1), where X(1)=max{X1,…,Xp}, and 00<c<1. In this paper, the simultaneous estimation of the Poisson means associated with the selected populations is considered for the k-normalized squared error loss function. It is shown that the natural estimator is positively biased. Also, a class of estimators that are better than the natural estimator is obtained by solving certain difference inequalities over the sample space. A class of estimators which dominate the UMVUE is also obtained. Monte carlo simulations are used to assess the percentage improvements and an application to a real-life example is also discussed. |
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Keywords: | Poisson populations Selected subset Estimation after selection Natural estimator Unbiased estimator Difference inequalities Improved estimators |
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