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April, 1987 A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options
F. Thomas Bruss, Stephen M. Samuels
Ann. Probab. 15(2): 824-830 (April, 1987). DOI: 10.1214/aop/1176992175

Abstract

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.

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F. Thomas Bruss. Stephen M. Samuels. "A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options." Ann. Probab. 15 (2) 824 - 830, April, 1987. https://doi.org/10.1214/aop/1176992175

Information

Published: April, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0592.60034
MathSciNet: MR885147
Digital Object Identifier: 10.1214/aop/1176992175

Subjects:
Primary: 60G40

Keywords: Bayes strategy , best choice problem , minimax strategy , noninformative prior , secretary problem

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 2 • April, 1987
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