Selecting Good Exponential Populations Compared with a Control: A Nonparametric Empirical Bayes Approach.
Abstract
This paper deals with empirical Bayes selection procedures for selecting good exponential populations compared with a control. Based on the accumulated historical data, an empirical Bayes selection procedure delta(*) is constructed by mimicking the behavior of a Bayes selection procedure. The empirical Bayes selection procedure delta(*) is proved to be asympototically optimal. The analysis shows that the rate of convergence of delta(*) is influenced by the tail probabilities of the underlying distributions. It is shown that under certain regularity conditions on the moments of the prior distribution, the empirical Bayes selection procedure delta(*) is asymptotically optimal of order O(n(-lambda/2)) for some 0<lambda<2. A lower bound with rate of convergence of order O(n(-1)) is also established for the regret Bayes risk of the empirical Bayes selection procedure delta(*). This result suggests that a rate of order O(n(-1)) might be the best possible rate of convergence for this empirical Bayes selection problem.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1996
- Accession Number
- ADA313657
Entities
People
- Shanti Gupta
- Tachen Liang
Organizations
- Purdue University