Date of this Version
The Annals of Probability
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.
The original and published work is available at: https://projecteuclid.org/euclid.aop/1176994265#abstract
monotone subsequence, optimal stopping, subadditive process
Samuels, S., & Steele, J. M. (1981). Optimal Sequential Selection of a Monotone Sequence From a Random Sample. The Annals of Probability, 9 (6), 937-947. http://dx.doi.org/10.1214/aop/1176994265
Date Posted: 27 November 2017
This document has been peer reviewed.