Statistics Papers

Document Type

Journal Article

Date of this Version

4-1981

Publication Source

The Annals of Probability

Volume

9

Issue

6

Start Page

937

Last Page

947

DOI

10.1214/aop/1176994265

Abstract

The length of the longest monotone increasing subsequence of a random sample of size n is known to have expected value asymptotic to 2n1/2. 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.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aop/1176994265#abstract

Comments

At the time of publication, author J. Michael Steele was affiliated with Stanford University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

Keywords

monotone subsequence, optimal stopping, subadditive process

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Date Posted: 27 November 2017

This document has been peer reviewed.