Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-12T20:30:00.270Z Has data issue: false hasContentIssue false
  • English
  • Français

On-line selection of an acceptable pair

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

J. Preater
J. Preater*
Affiliation:
Keele University
*
∗Postal address: Department of Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK. Email address: j.preater@keele.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A sequence of objects with independent, identically distributed qualities is presented to a selector who must choose two on-line, i.e. without anticipation or recall. The selector's aim is to obtain a satisfactory pair as quickly as possible. Two versions of the problem are considered, and optimal selection rules are derived and compared. An investigation is also made of a heuristic rule suitable for a selector who has no prior knowledge of the nature of the object sequence.

Keywords

Optimal stoppingmultiple selection

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 729 - 740
Copyright
© Applied Probability Trust 2006 

References

Assaf, D., Goldstein, L. and Samuel-Cahn, E. (2004). Two-choice optimal stopping. Adv. Appl. Prob. 36, 1116–1147.CrossRefGoogle Scholar
Chen, R. W., Nair, V. N. and Vardi, Y. (1984). Optimal sequential selection of N random variables under a constraint. J. Appl. Prob. 21, 537–547.Google Scholar
Chow, Y. S., Robbins, H. and Seigmund, D. (1971). Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston, MA.Google Scholar
Coffman, E. G. Jr., Flatto, L. and Weber, R. R. (1987). Optimal selection of stochastic intervals under a sum constraint. Adv. Appl. Prob. 19, 454–473.Google Scholar
Kennedy, D. P. and Kertz, R. P. (1992). Comparisons of optimal stopping values and expected suprema for iA.i.d. r.v.'s with costs and discounting. Contemp. Math. 125, 217–230.Google Scholar
Kühne, R. and Rüschendorf, L. (2002). On optimal two-stopping problems. In Limit Theorems in Probability and Statistics, Vol. II, János Bolyai Mathematical Society, Budapest, pp. 261–271.Google Scholar
Lippman, S. A. and McCall, J. J. (1976). The economics of Job search: a survey: part I. Econom. Enquiry 14, 155–189.Google Scholar
Preater, J. (1993). A note on monotonicity in optimal multiple stopping problems. Statist. Prob. Lett. 16, 407–410.CrossRefGoogle Scholar
Ramsey, D. M. (1994). Models of evolution, interaction and learning in sequential decision processes. , University of Bristol.Google Scholar
Tamaki, M. (1988). A Bayesian approach to the best-choice problem. J. Amer. Statist. Soc. 83, 1129–1133.Google Scholar