Abstract
The problem of statistical selection of a population with the largest mean value is considered. We introduce a sequential selection procedure, which we call first-crossing look-ahead (FCLA), for a normal-normal Bayesian setting of the problem, where variances of the populations are supposed to be the same and known, and the means are realizations of prior normal random variables with known distribution parameters. The paper includes the definition of the procedure with some basic analytical results, the results of numerical simulations, and a numerical performance comparison (in terms of sample size) with one of known efficient selection procedure for an indifference-zone setting of the selection problem.
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References
R. E. Bechhofer, “A single-sample multiple decision procedure for ranking means of normal populations with known variances,” Ann. Math. Statist. 25, 16–39 (1954).
S. S. Gupta, On a Decision Rule for a Problem in Ranking Means (Univ. of North Carolina, Chapel Hill, 1956).
S. Kao and T. T. Lai, “Sequential selection procedures based on confidence sequences for normal populations,” Commun. Stat.-Theor. Meth. A9, 1657–1676 (1980).
P. A. Pepple and S. C. Choi, “Bayesian approach to two-stage phase trial,” J. Biopharm. Stat. 7, 271–286 (1997).
S. E. Chick and K. Inoue, “New two-stage and sequential procedures for selecting the best simulated system,” Operat. Res. 49, 732–743 (2001).
P. I. Frazier, “A fully sequential elimination procedure for indifference-zone ranking and selection with tight bounds on probability of correct selection,” Operat. Res. 62, 926–942 (2014).
N. C. Henderson and M. A. Newton, “Making the cut: improved ranking and selection for large-scale inference,” J. R. Stat. Soc., Ser. B 78, 781–804 (2016).
R. Salimov, “A sequential d-guaranteed test for distinguishing two interval hypotheses,” Lobachevskii J. Math. 37, 500–503 (2016).
D. S. Simushkin, S. V. Simushkin, and I. N. Volodin, “D-guaranteed discrimination of statistical hypotheses: a review of results and unsolved problems,” J. Math. Sci. (U.S.) 228, 543–565 (2018).
J. O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd ed. (Springer, New York, 1985).
S. S. Gupta and K. J. Miescke, “Bayesian look ahead one stage sampling allocations for selecting the largest normal mean,” Stat. Papers 35, 169–177 (1994).
S. S. Gupta and K. J. Miescke, “Bayesian look ahead one-stage sampling allocations for selection of the best population,” J. Stat. Planning Inference 54, 229–244 (1996).
Funding
This study was funded by the Russian Foundation for Basic Research, project no. 18-31-00094.
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Kareev, I.A., Zaikin, A.A. Sequentual First-Crossing Look-Ahead Procedure for Selecting a Population with the Largest Meanin Normal-Normal Model. Lobachevskii J Math 40, 1178–1185 (2019). https://doi.org/10.1134/S1995080219080134
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DOI: https://doi.org/10.1134/S1995080219080134