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Easily determining which urns are ’favorable’. (English) Zbl 0613.62106

The optimal sampling strategy for an urn, containing known numbers of plus and minus ones, can be simply described with the use of an empirically justified rule, based upon what appears to be a legitimate third-order asymptotic expansion of ”the optimal stopping boundary” as the urn size goes to infinity. The rule performs exceedingly well. There is a known first-order asymptotic expansion due to L. A. Shepp [Ann. Math. Stat. 40, 993-1010 (1969; Zbl 0177.223)]. The reader is invited to try to justify a second-order asymptotic expansion of a type described by H. Chernoff and H. J. Petkau [Ann. Probab. 4, 875-889 (1976; Zbl 0347.62064)]. The evidence presented in its support is very persuasive.

MSC:

62L15 Optimal stopping in statistics
60C05 Combinatorial probability
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References:

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