Abstract
Abstract An asymptotically minimax simple sequential procedure for selection of the cells corresponding to the t highest multinomial cell probabilities has been given. It is found that the procedure performs uniformly better than the other two conventional procedures, namely the inverse sampling procedure and the fixed-sample-size procedure. For t=1, this proves some conjectures of Alam (Technometrics 13 (1971) 843–850). For t⩾1, derivations of least favorable configurations are immediate for the above-mentioned procedures with different indifference zones and with the number of observations tending to ∞. These also provide a simple proof of various main results in Bhandari and Bose (J. Statist. Plann. Inference 17 (1987) 227–240, Comm. Statist. Theory Methods 18 (1989) 3313–3326), Chen and Sobel (IMS Lecture Notes—Monograph Series 5 (1984) 206–210), Cacoullos and Sobel (Proc. 1 st Internat. Symp. on Multivariate Analysis (1966)) and Kesten and Morse (Ann. Math. Statist. 30 (1959) 120–127).
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