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August 1996 Optimal selection problems based on exchangeable trials
Alexander V. Gnedin, Ulrich Krengel
Ann. Appl. Probab. 6(3): 862-882 (August 1996). DOI: 10.1214/aoap/1034968230


We consider optimal stopping problems with loss function q depending on the rank of the stopped random variable. Samuels asked whether there exists an exchangeable sequence of random variables $X_1, \dots, X_n$ without ties for which the observation of the values of the $X_i$'s gives no advantage in comparison with the observation of just the relative ranks of the variables. We call distributions of the sequences with this property q-noninformative and derive necessary and sufficient conditions for this property. Extending an impossibility result of B. Hill, we show that, for any $n > 1$, there are certain losses q for which q-noninformative distributions do not exist. Special attention is given to the classical problem of minimizing the expected rank: for n even we construct explicitly universal randomized stopping rules which are strictly better than the rank rules for any exchangeable sequence.


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Alexander V. Gnedin. Ulrich Krengel. "Optimal selection problems based on exchangeable trials." Ann. Appl. Probab. 6 (3) 862 - 882, August 1996.


Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0903.60034
MathSciNet: MR1410118
Digital Object Identifier: 10.1214/aoap/1034968230

Primary: 60G40

Keywords: exchangeability , Optimal stopping , ‎rank‎ , secretary problems

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 3 • August 1996
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