Closed inverse sampling procedure for selecting the largest multinomial cell probability

Pinyuen Chen

doi:10.1080/03610918808812707

Closed inverse sampling procedure for selecting the largest multinomial cell probability

Pinyuen Chen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A class of closed inverse sampling procedures R(n,m) for selecting the multinomial cell with the largest probability is considered; here n is the maximum sample size that an experimenter can take and m is the maximum frequency that a multinomial cell can have. The proposed procedures R(n,m) achieve the same probability of a correct selection as do the corresponding fixed sample size procedures and the curtailed sequential procedures when m is at least n/2. A monotonicity property on the probability of a correct selection is proved and it is used to find the least favorable configurations and to tabulate the necessary probabilities of a correct selection and corresponding expected sample sizes.

Original language	English (US)
Pages (from-to)	969-994
Number of pages	26
Journal	Communications in Statistics - Simulation and Computation
Volume	17
Issue number	3
DOIs	https://doi.org/10.1080/03610918808812707
State	Published - Jan 1 1988

Keywords

curtailment procedure
inverse sampling procedure
least favorable configuration
multinomial selection problem

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation

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title = "Closed inverse sampling procedure for selecting the largest multinomial cell probability",

abstract = "A class of closed inverse sampling procedures R(n,m) for selecting the multinomial cell with the largest probability is considered; here n is the maximum sample size that an experimenter can take and m is the maximum frequency that a multinomial cell can have. The proposed procedures R(n,m) achieve the same probability of a correct selection as do the corresponding fixed sample size procedures and the curtailed sequential procedures when m is at least n/2. A monotonicity property on the probability of a correct selection is proved and it is used to find the least favorable configurations and to tabulate the necessary probabilities of a correct selection and corresponding expected sample sizes.",

keywords = "curtailment procedure, inverse sampling procedure, least favorable configuration, multinomial selection problem",

author = "Pinyuen Chen",

note = "Funding Information: This article is supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University. The author wishes to thank Professor Robert Bechhofer for many helpful suggestions and comments.",

year = "1988",

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T1 - Closed inverse sampling procedure for selecting the largest multinomial cell probability

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N1 - Funding Information: This article is supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University. The author wishes to thank Professor Robert Bechhofer for many helpful suggestions and comments.

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N2 - A class of closed inverse sampling procedures R(n,m) for selecting the multinomial cell with the largest probability is considered; here n is the maximum sample size that an experimenter can take and m is the maximum frequency that a multinomial cell can have. The proposed procedures R(n,m) achieve the same probability of a correct selection as do the corresponding fixed sample size procedures and the curtailed sequential procedures when m is at least n/2. A monotonicity property on the probability of a correct selection is proved and it is used to find the least favorable configurations and to tabulate the necessary probabilities of a correct selection and corresponding expected sample sizes.

AB - A class of closed inverse sampling procedures R(n,m) for selecting the multinomial cell with the largest probability is considered; here n is the maximum sample size that an experimenter can take and m is the maximum frequency that a multinomial cell can have. The proposed procedures R(n,m) achieve the same probability of a correct selection as do the corresponding fixed sample size procedures and the curtailed sequential procedures when m is at least n/2. A monotonicity property on the probability of a correct selection is proved and it is used to find the least favorable configurations and to tabulate the necessary probabilities of a correct selection and corresponding expected sample sizes.

KW - curtailment procedure

KW - inverse sampling procedure

KW - least favorable configuration

KW - multinomial selection problem

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