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A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options

par Bruss, F Thomas ;Samuels, Stephen M.
Référence Annals of probability, 15, 2, page (824-830)
Publication Publié, 1987-04

Article révisé par les pairs

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Résumé :

In the so-called secretary problem, if an unknown number, N, of options arrive at i.i.d. times with a known continuous distribution, then ignorance of how many options there are becomes almost irrelevant: The optimal rule for infinitely many options is shown to be minimax with respect to all possible distributions of N, nearly optimal whenever N is likely to be large, and formal Bayes against a noninformative prior. These results hold whatever the loss function.