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Let Π1, …, Π p be p(p≥2) independent Poisson populations with unknown parameters θ1, …, θ p , respectively. Let X i denote an observation from the population Π i , 1≤i≤p. Suppose a subset of random size, which includes the best population corresponding to the largest (smallest) θ i , is selected using Gupta and Huang [On subset selection procedures for Poisson populations and some applications to the multinomial selection problems, in Applied Statistics, R.P. Gupta, ed., North-Holland, Amsterdam, 1975, pp. 97–109] and (Gupta et al. [On subset selection procedures for Poisson populations, Bull. Malaysian Math. Soc. 2 (1979), pp. 89–110]) selection rule. In this paper, the problem of estimating the average worth of the selected subset is considered under the squared error loss function. The natural estimator is shown to be biased and the UMVUE is obtained using Robbins [The UV method of estimation, in Statistical Decision Theory and Related Topics-IV, S.S. Gupta and J.O. Berger, eds., Springer, New York, vol. 1, 1988, pp. 265–270] UV method of estimation. The natural estimator is shown to be inadmissible, by constructing a class of dominating estimators. Using Monte Carlo simulations, the bias and risk of the natural, dominated and UMVU estimators are computed and compared. 相似文献
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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 0<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. 相似文献
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