INADMISSIBILITY RESULTS FOR THE SELECTED SCALE-PARAMETERS

• 成果类型: Article
• 署名作者: VELLAISAMY, P
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348913
• 发表日期: 1992
• 页码: 2183-2191
• 关键词: exponential-families; estimators; population

摘要

Let X1, X2,..., X(k) be k independent gamma random variables with different scale parameters but with a common known shape parameter. Suppose the population corresponding to the largest X(1) [or the smallest X(k)] observation is selected. The problem of estimating the scale parameter theta(1) [or theta(k)] of the selected population is considered. We derive, using the method of differential inequalities, explicit estimators that dominate the natural or the existing estimators. The improved estimators of theta(1) are similar to that of DasGupta estimators for the usual simultaneous estimation problem. An implication of this result for the simultaneous estimation of the selected subset is also considered.