Open Access
January, 1991 Minimax-Optimal Stop Rules and Distributions in Secretary Problems
Theodore P. Hill, Ulrich Krengel
Ann. Probab. 19(1): 342-353 (January, 1991). DOI: 10.1214/aop/1176990548


For the secretary (or best-choice) problem with an unknown number $N$ of objects, minimax-optimal stop rules and (worst-case) distributions are derived, under the assumption that $N$ is a random variable with unknown distribution, but known upper bound $n$. Asymptotically, the probability of selecting the best object in this situation is of order of $(\log n)^{-1}$. For example, even if the only information available is that there are somewhere between 1 and 100 objects, there is still a strategy which will select the best item about one time in five.


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Theodore P. Hill. Ulrich Krengel. "Minimax-Optimal Stop Rules and Distributions in Secretary Problems." Ann. Probab. 19 (1) 342 - 353, January, 1991.


Published: January, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0723.60043
MathSciNet: MR1085340
Digital Object Identifier: 10.1214/aop/1176990548

Primary: 60G40
Secondary: 62C20 , 90D05

Keywords: best-choice problem , marriage-problem , minimax-optimal distribution , minimax-optimal stop rule , randomized stop rule , secretary problem

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • January, 1991
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