Vanishing shortcoming and asymptotic relative efficiency

• 成果类型: Article
• 署名作者: Inglot, T; Kallenberg, WCM; Ledwina, T
• 署名单位: Wroclaw University of Science & Technology; University of Twente; Polish Academy of Sciences
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 215-238
• 关键词: kolmogorov-smirnov test; POWER

摘要

The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly stronger than first-order efficiency, but in regular eases there is equivalence. The results are in particular applied to tests for goodness-of-fit.