## The Annals of Probability

### Optimal Sequential Selection of a Monotone Sequence From a Random Sample

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 9, Number 6 (1981), 937-947.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994265

Digital Object Identifier
doi:10.1214/aop/1176994265

Mathematical Reviews number (MathSciNet)
MR632967

Zentralblatt MATH identifier
0473.62073

JSTOR