Truncation of the bechhofer-kiefer-sobel sequential procedure for selecting the multinomial event which has the largest probability (ii): extended tables and an improved procedure

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Abstract
In an earlier article the authors studied the performance of a truncated version of a vector-at-a-time sequential sampling procedure proposed by Bechhofer, Kiefer and Sobel for selecting the multinomial event which has the largest probability. Among the performance characteristics studied for both the original (open) basic procedure (P*B:) and the truncated (closed) procedure (P*B:T:) were the achieved probability of a correct selection, and BT the expected number of vector-observations (n) to terminate sampling when the event probabilities are in the so-called least-favorable and equal-parameter configurations. These were compared with the same quantities for a competing (closed) procedure of Ramey and Alam (R-A). All three procedures guarantee the same requirement on the probability of a correct selection. The truncated procedure was shown to be greatly superior to the untruncated version both in terms of E{n} and Var{n}, and also to be superior to the R-A procedure.¶A limited set of truncation numbers (n0:) necessary to implement P*B:T:, and associated performance characteristics of P*B:T:, were given in our earlier article. In the present article BT we supply a greatly expanded set of n0:-values and associated performance characteristics. The tables presented herein are sufficiently detailed to enable implementation of P*B:T: over a broad range of specifications, and should be sufficient for all practical purposes. A method of interpolating in the tables is given, thereby extending their domain of usefulness.¶We also describe an improved version of the truncated procedure (P*B:T:(I:)) and give its performance characteristics. The dis- BT(Distribution of n for P*B:T:(I:) is stochastically smaller (never BT(D larger) than that for P*B:T: for almost all (for any) values of the BT specified constants. As a consequence, E{n} is decreased, uniformly in the unknown event probabilities, although in most instances the decrease is rather small.