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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/10190
Title: Estimating average worth of the selected subset from two-parameter exponential populations
Authors: Gangopadhyay, Aditi Kar
Kumar S.
Published in: Communications in Statistics - Theory and Methods
Abstract: Suppose independent random samples are available from k ( k ≥ 2) exponential populations ∠1 , ⋯ , ∠k with a common location θ and scale parameters σ1 , ⋯ , σk, respectively. Let Xi and Yi denote the minimum and the mean, respectively, of the i th sample, and further let X = min{X1 , ⋯ , Xk} and Ti = Yi - X ; i = 1, ⋯ , k . For selecting a nonempty subset of {∠1 , ⋯ ,∠k} containing the best population (the one associated with max{σ1 , ⋯ , σk}), we use the decision rule which selects ∠i if Ti ≥ c max{T1, ⋯ , Tk}, i = 1, ⋯ , k. Here 0 < c ≤ 1 is chosen so that the probability of including the best population in the selected subset is at least P* (1/k ≤ P* < 1), a pre-assigned level. The problem is to estimate the average worth W of the selected subset, the arithmetic average of means of selected populations. In this article, we derive the uniformly minimum variance unbiased estimator (UMVUE) of W. The bias and risk function of the UMVUE are compared numerically with those of analogs of the best affine equivariant estimator (BAEE) and the maximum likelihood estimator (MLE).
Citation: Communications in Statistics - Theory and Methods (2005), 34(12): 2257-2267
URI: https://doi.org/10.1080/03610920500257220
http://repository.iitr.ac.in/handle/123456789/10190
Issue Date: 2005
Keywords: Average worth
Best affine equivariant estimator
Exponential populations
Subset selection
Uniformly minimum variance unbiased estimator
ISSN: 3610926
Author Scopus IDs: 10540368200
55490017200
Author Affiliations: Gangopadhyay, A.K., Department of Mathematics, Indian Institute of Technology, Roorkee, India, Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India
Kumar, S., Department of Mathematics, Indian Institute of Technology, Kharagpur, India
Corresponding Author: Gangopadhyay, A.K.; Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India; email: aditifma@iitr.ernet.in
Appears in Collections:Journal Publications [MA]

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