Closed sequential procedures for selecting the multinomial events which have the largest probabilities
Titel:
Closed sequential procedures for selecting the multinomial events which have the largest probabilities
Auteur:
Bechhofer, Robert E. Kulkarni, Radhika V.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 13 (1984) nr. 24 pagina's 2997-3031
Jaar:
1984
Inhoud:
Single-stage and closed sequential procedures for selecting the multinomial events which have the largest probabilities areconsidered. Two goals, Goal I (Selecting the s [image omitted] best categories without regard to order) and Goal II (Selecting the s [image omitted] best categories with regard to order) are studied in detail; here k ≥ 2 is the number of categories in the multjinomial distribution. Goal I includes as special cases, the goals of Bechhofer, Elmaghraby and Morse (1959) and Alam and Thompson (1972) which correspond here to the cases s = 1 and s = k-l, respectively; both foregoing articles gave single-stage procedures whi ch when used with an appropri ate si ng1e-stage slamp1e size n guarantee a probability requirement which employs the Isocalled indifference-zone approach. The sequenti a1 procedures tha t we propose achi eve the same probability of a correct selection as do the corresponding silngle stage procedures, uniformly in the unknown event probabilities [image omitted] . Moreover, this is accomplished with a smaller expected number of vector-observations than that required by the corresponding single-stage procedures. The properties of these sequential procedures. The properties of these sequential procedures are studied analytically, and tables are provided which show the savings in expected sample size when they are used in place of the corresponding single-stage procedures. Comparisons are also made with the expected sample size required by a curtailed sequential procedure proposed by Gibbons, Olkin and Sobel (1977), and it is demonstrated that our sequential procedures are uniformly superior to theirs in terms of expected number of vector-observations.
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