## The Annals of Probability

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

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

F. Thomas Bruss and Stephen M. Samuels

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

**Keywords**

Best choice problem secretary problem minimax strategy Bayes strategy noninformative prior

#### Citation

Bruss, F. Thomas; Samuels, Stephen M. A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options. Ann. Probab. 15 (1987), no. 2, 824--830. doi:10.1214/aop/1176992175. https://projecteuclid.org/euclid.aop/1176992175