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
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.
Ann. Probab., Volume 15, Number 2 (1987), 824-830.
First available in Project Euclid: 19 April 2007
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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