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The secretary problem with an unknown number of candidates

Published online by Cambridge University Press:  14 July 2016

A. R. Abdel-hamid ,
J. A. Bather  and
G. B. Trustrum
A. R. Abdel-hamid*
Affiliation:
University of Sussex
J. A. Bather*
Affiliation:
University of Sussex
G. B. Trustrum*
Affiliation:
University of Sussex
*
∗Postal address: School of Mathematical and Physical Sciences, The University of Sussex, Falmer, Brighton BN1 9QH, U.K.
∗Postal address: School of Mathematical and Physical Sciences, The University of Sussex, Falmer, Brighton BN1 9QH, U.K.
∗Postal address: School of Mathematical and Physical Sciences, The University of Sussex, Falmer, Brighton BN1 9QH, U.K.
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Abstract

When the number of candidates is unknown, the problem of selecting the best during a sequence of interviews has many reasonable solutions. A simple condition for admissibility is established and it is shown that the class of Bayes solutions obtained by treating the number of candidates as a random variable is by no means complete. On the other hand, there is a single improper prior distribution for which the extended Bayes solutions constitute the whole family of admissible procedures.

Keywords

SECRETARY PROBLEMMARRIAGE PROBLEMOPTIMAL STOPPINGADMISSIBILITYSTATISTICAL DECISION THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 619 - 630
Copyright
Copyright © Applied Probability Trust 1982 

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