The Annals of Probability

Minimax-Optimal Stop Rules and Distributions in Secretary Problems

Theodore P. Hill and Ulrich Krengel

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Abstract

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.

Article information

Source
Ann. Probab., Volume 19, Number 1 (1991), 342-353.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990548

Digital Object Identifier
doi:10.1214/aop/1176990548

Mathematical Reviews number (MathSciNet)
MR1085340

Zentralblatt MATH identifier
0723.60043

JSTOR
links.jstor.org

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 62C20: Minimax procedures 90D05

Keywords
Secretary problem best-choice problem marriage-problem minimax-optimal stop rule minimax-optimal distribution randomized stop rule

Citation

Hill, Theodore P.; Krengel, Ulrich. Minimax-Optimal Stop Rules and Distributions in Secretary Problems. Ann. Probab. 19 (1991), no. 1, 342--353. doi:10.1214/aop/1176990548. https://projecteuclid.org/euclid.aop/1176990548


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