Closed inverse sampling procedure for selecting the largest multinomial cell probability

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.