Abstract
Suppose a subset of populations is selected from the given k gamma G(θ i,p ) (i = 1,2,...,k)populations, using Gupta's rule (1963, Ann. Inst. Statist. Math., 14, 199–216). The problem of estimating the average worth of the selected subset is first considered. The natural estimator is shown to be positively biased and the UMVUE is obtained using Robbins' UV method of estimation (1988, Statistical Decision Theory and Related Topics IV, Vol. 1 (eds. S. S. Gupta and J. O. Berger), 265–270, Springer, New York). A class of estimators that dominate the natural estimator for an arbitrary k is derived. Similar results are observed for the simultaneous estimation of the selected subset.
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References
Berger, J. O. (1980). Improving on inadmissible estimators in continuous exponential families with applications to simultaneous estimation of gamma scale parameters, Ann. Statist., 8, 545–571.
Brewster, J. F. and Zidek, J. V. (1974). Improving on equivariant estimators, Ann. Statist., 2, 21–38.
Cohen, A. and Sackrowitz, H. (1982). Estimating the mean of the selected population, Statistical Decision Theory and Related topics-III, Vol. 1 (eds. S. S.Gupta and J. O.Berger), 243–270, Academic Press, New York.
Cohen, A. and Sackrowitz, H. (1989). Two stage conditionally unbiased estimators of the selected mean, Statist. Probab. Lett., 8, 273–278.
Gupta, S. S. (1963). On a selection and ranking procedure for gamma population, Ann. Inst. Statist. Math., 14, 199–216.
Jeyarathnam, S. and Panchapakesan, S. (1984). An estimation problem relating to subset selection for normal populations, Design of Experiments: Ranking and Selection (eds. T. J.Santner and A. C.Tamhane), Dekker, New York.
Jeyarathnam, S. and Panchapakesan, S. (1986). Estimation after subset selection from exponential populations, Comm. Statist. Theory Methods, 15, 3459–3473.
Lehmann, E. L. (1983). Theory of Point Estimation, Wiley, New York.
Robbins, H. E. (1988). The UV method of estimation, Statistical Decision Theory and Related Topics IV, Vol. 1 (eds. S. S.Gupta and J. O.Berger), 265–270, Springer, New York.
Sackrowitz, H. and Samuel-Cahn, E. (1984). Estimation of the mean of a selected negative exponential population, J. Roy. Statist. Soc. Ser. B, 46, 242–249.
Sackrowitz, H. and Samuel-Cahn, E. (1987). Evaluating the chosen population: a Bayes and minimax approach, Adaptive Statistical Procedures and Related Topics, IMS Lecture Notes—Monograph Series, Vol. 8, 386–399, Hayward, California.
Vellaisamy, P. and Sharma, D. (1990). On estimation after subset selection from exponential populations, Sankhyā Ser. B, 52, 305–318.
Venter, J. H. (1988). Estimation of the mean of the selected population, Comm. Statist. Theory Methods, 17, 797–805.
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Vellaisamy, P. Average worth and simultaneous estimation of the selected subset. Ann Inst Stat Math 44, 551–562 (1992). https://doi.org/10.1007/BF00050705
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DOI: https://doi.org/10.1007/BF00050705