On a Lower Confidence Bound for the Probability of a Correct Selection: Analytical and Simulation Studies.
Abstract
For the problem of selecting the best of several populations using the indifference (preference) zone formulation, a natural rule is to select the population yielding the largest sample value of an appropriate statistic. For this approach, it is required that the experimenter specify a number delta*, say, which is a lower bound on the difference (separation) between the largest and the second largest parameter. However, in many real situations, it is hard to assign the value of delta* and, therefore, in case that the assumption of indifference zone is violate, the probability of a correct selection cannot be guaranteed to be at least P*, a prespecified value. This paper concerns the derivation of a lower confidence bound for the probability of a correct selection for the general location model F(x-Theta), i = l,...,k. First, derive simultaneous lower confidence bounds on the differences between the largest (best) and each of the other non-best population parameters. Based on these, a lower confidence bound is obtained for the probability of a correct selection. The general result is then applied to the selection of the best mean of k normal populations with both the known and unknoWn common variances. In the first case one needs a single stage procedure while in the second case a two stage procedure is required. Some simulation investigations are described and their results are provided.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1987
- Accession Number
- ADA181066
Entities
People
- Shanti Gupta
- Tachen Liang
Organizations
- Purdue University