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Abstract
This paper considers the problem of selecting the cell with the largest cell probability of multinomial distribution when one of the cells is considered as nuisance cell. A multinomial distribution is supposed to have three cells for the first attempt to this problem. A Stein-type two-stage procedure is proposed to select the best cell under the two types of indifference-zone formulation in ranking and selection theory. We first identify the configuration at which the probability of correct selection is minimum under the fixed-sample size procedure when the nuisance cell probability is fixed. Then we propose a two-stage procedure to (1) estimate the nuisance cell probability in the first stage, and (2) select the best cell in the second stage. It is shown that the proposed two-stage procedure is asymptotically efficient. The tables of the procedure parameters are provided and a Monte Carlo simulation is given to illustrate the efficiency of the procedure.