OPTIMAL SELECTION PROBLEMS BASED ON EXCHANGEABLE TRIALS
成果类型：
Article
署名作者：
Gnedin, Alexander V.; Krengel, Ulrich
署名单位：
University of Gottingen
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
862-882
关键词：
摘要：
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,..., 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.