Closed sequential procedures for selecting the multinomial events which have the largest probabilities

Single-stage and closed sequential procedures for selecting the multinomial events which have the largest probabilities areconsidered. Two goals, Goal I (Selecting the s best categories without regard to order) and Goal II (Selecting the s 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 . Moreover, this is accomplished with a smaller expected nu...

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