Truncation of the Bechhofer-Kiefer-Sobel sequential procedure for selecting the multinomial event which has the largest probability.

*(English)*Zbl 0583.62023The effect of truncation is studied on the performance of an open vector- at-a-time sequential sampling procedure [R. E. Bechhofer, J. Kiefer and M. Sobel, Sequential identification and ranking procedures, with special references to Koopman-Darmois populations (1968; Zbl 0208.446)], for selecting the multinomial event which has the largest probability.

It is shown that the truncated version is far superior to the original version in terms of the expected number of vector-observations (n) to terminate sampling and of the variance of n uniformly in the event probabilities, and that the improvement is greatest when they are equal.

Both exact results and Monte Carlo sampling results are presented. The performance of the truncated version is also compared to that of a closed vector-at-a-time sequential sampling procedure; cf. J. T. Ramey and K. Alam, A sequential procedure for selecting the most probable multinomial event. Biometrika, 66, 171-173 (1979).

It is shown that the truncated version is far superior to the original version in terms of the expected number of vector-observations (n) to terminate sampling and of the variance of n uniformly in the event probabilities, and that the improvement is greatest when they are equal.

Both exact results and Monte Carlo sampling results are presented. The performance of the truncated version is also compared to that of a closed vector-at-a-time sequential sampling procedure; cf. J. T. Ramey and K. Alam, A sequential procedure for selecting the most probable multinomial event. Biometrika, 66, 171-173 (1979).

Reviewer: K.Uosaki

##### Keywords:

Bechhofer-Kiefer-Sobel sequential procedure; multinomial selection; ranking procedures; truncation; open vector-at-a-time sequential sampling procedure; largest probability; exact results; Monte Carlo sampling results
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\textit{R. E. Bechhofer} and \textit{D. M. Goldsman}, Commun. Stat., Simulation Comput. 14, 283--315 (1985; Zbl 0583.62023)

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##### References:

[1] | Bechhofer R.E., Ann. Math. Statist 30 pp 102– (1959) · Zbl 0218.62064 · doi:10.1214/aoms/1177706362 |

[2] | Bechhofer R.E., Comro. Statist.–Simula. Computa., B14, this issue, preceding article 30 (1985) |

[3] | Bechhofer R.E., (with special reference to Koopman-Darmois populations) |

[4] | Bechhofer R.E., Commun. Statist.–Theor. Meth. A 13 (24) pp 2997– (1984) · Zbl 0571.62069 · doi:10.1080/03610928408828875 |

[5] | Gibbons, J.D., Olkin, I. and Sobel, M. ”Selecting and Ordering Populations”. · Zbl 0464.62022 |

[6] | IMSL Manual (1982) |

[7] | Kesten H., Ann. Math. Statist 30 pp 120– (1959) · Zbl 0218.62017 · doi:10.1214/aoms/1177706363 |

[8] | Levin B., Kiefer and Sobel. Statistics and Probability Letters pp 91– |

[9] | Ramey J.T., Biometrika 66 pp 171– (1979) · doi:10.1093/biomet/66.1.171 |

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