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Online Selection of Alternating Subsequences from a Random Sample

Part of: Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Alessandro Arlotto ,
Robert W. Chen ,
Lawrence A. Shepp  and
J. Michael Steele
Alessandro Arlotto*
Affiliation:
University of Pennsylvania
Robert W. Chen*
Affiliation:
University of Miami
Lawrence A. Shepp*
Affiliation:
University of Pennsylvania
J. Michael Steele*
Affiliation:
University of Pennsylvania
*
∗ Postal address: Wharton School, Department of Operations and Information Management, Huntsman Hall 527.2, University of Pennsylvania, Philadelphia, PA 19104, USA. Email address: alear@wharton.upenn.edu
∗∗ Postal address: Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA. Email address: chen@math.miami.edu
∗∗∗ Postal address: Wharton School, Department of Statistics, Huntsman Hall 462, University of Pennsylvania, Philadelphia, PA 19104, USA. Email address: shepp@wharton.upenn.edu
∗∗∗∗ Postal address: Wharton School, Department of Statistics, Huntsman Hall 447, University of Pennsylvania, Philadelphia, PA 19104, USA. Email address: steele@wharton.upenn.edu
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Abstract

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We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, we find (in a sense we make precise) that a person who is constrained to make sequential selections does only about 12 percent worse than a person who can make selections with full knowledge of the random sequence.

Keywords

Bellman equationonline selectionsequential selectionprophet inequalityalternating subsequence

MSC classification

Secondary: 60C05: Combinatorial probability 90C40: Markov and semi-Markov decision processes 90C27: Combinatorial optimization 90C39: Dynamic programming
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 1114 - 1132
Copyright
Copyright © Applied Probability Trust 2011 

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