A Restricted Subset Selection Approach to Ranking and Selection Problems
Santner, Thomas J.
Ann. Statist., Tome 3 (1975) no. 1, p. 334-349 / Harvested from Project Euclid
Let $\pi_1,\cdots, \pi_k$ be $k$ populations with $\pi_i$ characterized by a scalar $\lambda_i \in \Lambda$, a specified interval on the real line. The object of the problem is to make some inference about $\pi_{(k)}$, the population with largest $\lambda_i$. The present work studies rules which select a random number of populations between one and $m$ where the upper bound, $m$, is imposed by inherent setup restrictions of the subset selection and indifference zone approaches. A selection procedure is defined in terms of a set of consistent sequences of estimators for the $\lambda_i$'s. It is proved the infimum of the probability of a correct selection occurs at a point in the preference zone for which the parameters are as close together as possible. Conditions are given which allow evaluation of this last infimum. The number of non-best populations selected, the total number of populations selected, and their expectations are studied both asymptotically and for fixed $n$. Other desirable properties of the rule are also studied.
Publié le : 1975-03-14
Classification:  Ranking and selection,  restricted subset size,  multiple decision,  62F07,  62G30
@article{1176343060,
     author = {Santner, Thomas J.},
     title = {A Restricted Subset Selection Approach to Ranking and Selection Problems},
     journal = {Ann. Statist.},
     volume = {3},
     number = {1},
     year = {1975},
     pages = { 334-349},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343060}
}
Santner, Thomas J. A Restricted Subset Selection Approach to Ranking and Selection Problems. Ann. Statist., Tome 3 (1975) no. 1, pp.  334-349. http://gdmltest.u-ga.fr/item/1176343060/