A unified approach to a class of optimal selection problems with an unknown number of options
type: Item
instance of: scholarly article
title: A unified approach to a class of optimal selection problems with an unknown number of options
zbMATH Open document ID: 0592.60034
author: Stephen M. Samuels
author: F. Thomas Bruss
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: 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 non-informative prior. These results hold whatever the loss function.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G25
Mathematics Subject Classification ID: 62M20
zbMATH DE Number: 3951700
zbMATH Keywords: best choice problem
zbMATH Keywords: minimax strategy
zbMATH Keywords: Bayes strategy
zbMATH Keywords: non-informative prior
zbMATH Keywords: secretary problem
zbMATH Keywords: infinitely many options
zbMATH Keywords: loss function
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992175
OpenAlex ID: W2011783211
DOI: 10.1214/AOP/1176992175
description: scientific article; zbMATH DE number 3951700