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A full-information best-choice problem with finite memory

Published online by Cambridge University Press:  14 July 2016

Mitsushi Tamaki
Mitsushi Tamaki*
Affiliation:
Otemon Gakuin University
*
∗Present address: Department of Law and Economics, Aichi University, Toyohashi-city, Aichi, Japan.
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Abstract

n i.i.d. random variables with known continuous distribution are observed sequentially with the objective of selecting the largest. This paper considers the finite-memory case which, at each stage, allows a solicitation of anyone of the last m observations as well as of the present one. If the (k – t)th observation with value x is solicited at the k th stage, the probability of successful solicitation is p1(x) or p2(x) according to whether t = 0 or 1 ≦ t ≦ m. The optimal procedure is shown to be characterized by the double sequences of decision numbers. A simple algorithm for calculating the decision numbers and the probability of selecting the largest is obtained in a special case.

Keywords

SECRETARY PROBLEMOPTIMAL STOPPING RULE
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 718 - 735
Copyright
Copyright © Applied Probability Trust 1986 

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References

Gilbert, J. P. and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73.CrossRefGoogle Scholar
Petruccelli, J. D. (1982) Full information best-choice problems with recall of observations and uncertainty of selection depending on the observation. Adv. Appl. Prob. 14, 340–358.CrossRefGoogle Scholar
Rubin, H. and Samuels, S. ?. (1977) The finite memory secretary problem. Ann. Prob. 5, 627–635.CrossRefGoogle Scholar
Sakaguchi, M. (1973) A note on the dowry problem. Rep. Statist. Appl. Res. JUSE 20, 11–17.Google Scholar
Samuels, S. M. (1981) An explicit formula for the limiting optimal success probability in the full information best choice problem. Purdue University Statistics Department Mimeograph Series.Google Scholar
Smith, M. H. and Deely, J. J. (1975) A secretary problem with finite memory. J. Amer. Statist. Assoc. 70, 357–361.CrossRefGoogle Scholar