The Annals of Probability

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

F. Thomas Bruss and Stephen M. Samuels

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 15, Number 2 (1987), 824-830.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992175

Digital Object Identifier
doi:10.1214/aop/1176992175

Mathematical Reviews number (MathSciNet)
MR885147

Zentralblatt MATH identifier
0592.60034

JSTOR
links.jstor.org

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Best choice problem secretary problem minimax strategy Bayes strategy noninformative prior

Citation

Bruss, F. Thomas; Samuels, Stephen M. A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options. Ann. Probab. 15 (1987), no. 2, 824--830. doi:10.1214/aop/1176992175. https://projecteuclid.org/euclid.aop/1176992175


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