## The Annals of Probability

### A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options

#### Abstract

In the so-called secretary problem, if an unknown number, $N$, of options arrive at i.i.d. times with a known continuous distribution, then ignorance of how many options there are becomes almost irrelevant: The optimal rule for infinitely many options is shown to be minimax with respect to all possible distributions of $N$, nearly optimal whenever $N$ is likely to be large, and formal Bayes against a noninformative prior. These results hold whatever the loss function.

#### Article information

Source
Ann. Probab., Volume 15, Number 2 (1987), 824-830.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992175

Digital Object Identifier
doi:10.1214/aop/1176992175

Mathematical Reviews number (MathSciNet)
MR885147

Zentralblatt MATH identifier
0592.60034

JSTOR