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On a best-choice problem by dependent criteria

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Alexander V. Gnedin
Alexander V. Gnedin*
Affiliation:
University of Göttingen
*
∗ Postal address: Institut für Mathematische Stochastik. Universität Göttingen, Lotzestrasse 13, D-3400 Göttingen, Germany.
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Abstract

We study the problem of maximizing the probability of stopping at an object which is best in at least one of a given set of criteria, using only stopping rules based on the knowledge of whether the current object is relatively best in each of the criteria. The asymptotic results for the case of independent criteria are shown to hold in certain cases where the componentwise maxima are, pairwise, either asymptotically independent or asymptotically full dependent.

An example of the former is a random sample from a bivariate correlated normal distribution; thus our results settle a question posed recently by T. S. Ferguson.

Keywords

STOPPING RULESMULTIVARIATE EXTREMES

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 221 - 234
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported by Deutsche Forschungsgemeinschaft.

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