Least favorable configuration and asymptotic efficiency of multinomial selection procedures

Inverse sampling procedures to select the cell corresponding to the highest multinomial cell probability have been studied and used widely in the literature. In this paper we establish the superiority of the inverse sampling procedure to the fixed sample size procedure over all configurations of cel...

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Bibliographic Details
Published in:Journal of statistical planning and inference 1994-04, Vol.39 (1), p.71-83
Main Authors: Bhandari, Subir Kumar, Sengupta, Debasis
Format: Article
Language:English
Subjects:
asymptotic relative efficiency
Decision theory
Exact sciences and technology
fixed size sampling
indifference zone
inverse sampling
Mathematics
Probability and statistics
Probability of correct selection
Sciences and techniques of general use
Statistics
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Summary:Inverse sampling procedures to select the cell corresponding to the highest multinomial cell probability have been studied and used widely in the literature. In this paper we establish the superiority of the inverse sampling procedure to the fixed sample size procedure over all configurations of cell probabilities in the asymptotic sense. This trend is empirically shown to prevail for small sample size as well. The results have also been used to derive the least favorable configurations (LFC) for the procedures over different indifference zones and as the number of observations tends to infinity. A byproduct of this approach is simpler proofs of several useful results in the literature.
ISSN:0378-3758
1873-1171
DOI:10.1016/0378-3758(94)90113-9