## The Annals of Probability

### Minimax-Optimal Stop Rules and Distributions in Secretary Problems

#### Abstract

For the secretary (or best-choice) problem with an unknown number $N$ of objects, minimax-optimal stop rules and (worst-case) distributions are derived, under the assumption that $N$ is a random variable with unknown distribution, but known upper bound $n$. Asymptotically, the probability of selecting the best object in this situation is of order of $(\log n)^{-1}$. For example, even if the only information available is that there are somewhere between 1 and 100 objects, there is still a strategy which will select the best item about one time in five.

#### Article information

Source
Ann. Probab., Volume 19, Number 1 (1991), 342-353.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990548

Digital Object Identifier
doi:10.1214/aop/1176990548

Mathematical Reviews number (MathSciNet)
MR1085340

Zentralblatt MATH identifier
0723.60043

JSTOR