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December, 1981 Optimal Sequential Selection of a Monotone Sequence From a Random Sample
Stephen M. Samuels, J. Michael Steele
Ann. Probab. 9(6): 937-947 (December, 1981). DOI: 10.1214/aop/1176994265


The length of the longest monotone increasing subsequence of a random sample of size $n$ is known to have expected value asymptotic to $2n^{1/2}$. We prove that it is possible to make sequential choices which give an increasing subsequence of expected length asymptotic to $(2n)^{1/2}$. Moreover, this rate of increase is proved to be asymptotically best possible.


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Stephen M. Samuels. J. Michael Steele. "Optimal Sequential Selection of a Monotone Sequence From a Random Sample." Ann. Probab. 9 (6) 937 - 947, December, 1981.


Published: December, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0473.62073
MathSciNet: MR632967
Digital Object Identifier: 10.1214/aop/1176994265

Primary: 62L15
Secondary: 60G40

Keywords: Monotone subsequence , Optimal stopping , subadditive process

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 6 • December, 1981
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