Moment-Based Minimax Stopping Functions for Sequences of Random Variables

Frans A. Boshuizen, Erasmus University of Rotterdam
Theodore P. Hill, Georgia Institute of Technology - Main Campus

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Copyright © 1992 Elsevier. The definitive version is available at http://dx.doi.org/10.1016/0304-4149(92)90064-W.

NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.

Abstract

Minimax-optimal stopping times and minimax (worst-case) distributions are found for the problem of stopping a sequence of uniformly bounded independent random variables, when only the means and/or variances are known, in contrast to the classical setting where the complete joint distributions of the random variables are known. Results are obtained for both the independent and i.i.d. cases, with applications given to the problem of order section in optimal stopping.