Minimax Subset Selection with Applications to Unequal Variance Problems.
Abstract
Let X(1),...,X(k) be observations from populations whose distributions are determined by unknown real parameters theta(1),..., theta(k). In a subset selection problem, the goal is to select a subset of the populations which includes the population associated with the largest parameter with 'high' probability and includes the other populations with 'low' probability. In this paper, rules are found which are minimax in the class of non-randomized, just, and translation invariant rules when risk is measured by the maximum probability of including a non-best population. These rules are of the form proposed and studied by Gupta in location and scale parameter problems. In many cases, these rules are the unique minimax rule in the class and, hence are also admissible in this class. These results are applied to the normal mean problem with known unequal variances (or unequal sample sizes). Comparison of several proposed rules is made. A rule proposed by Gupta and Huang is found to be minimax. A generalization of the rule, proposed by Gupta and Wong, is likewise minimax. Other rules, proposed by Chen and Dudewicz and Gupta and Huang are shown to be not minimax.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1977
- Accession Number
- ADA041744
Entities
People
- Roger L. Berger
- Shanti Gupta
Organizations
- Purdue University