ON ASYMPTOTICALLY OPTIMAL TESTS UNDER LOSS OF IDENTIFIABILITY IN SEMIPARAMETRIC MODELS

• 成果类型: Article
• 署名作者: Song, Rui; Kosorok, Michael R.; Fine, Jason P.
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS643
• 发表日期: 2009
• 页码: 2409-2444
• 关键词: PROPORTIONAL HAZARDS MODEL; likelihood ratio tests; nuisance parameter; regression-models; efficient estimation; change-point; hypothesis; inference; mixture; covariate

摘要

We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile likelihood are Constructed and shown to be asymptotically optimal under a weighted average power criterion with respect to a prior oil the nonidentifiable aspect of the model. These results extend existing results for parametric models, which involve more restrictive assumptions on the form of the alternative than do our results. Moreover, the proposed tests accommodate models with infinite dimensional nuisance parameters which either may not be identifiable or may not be estimable at the usual parametric rate. Examples include tests of the presence of a change-point in the Cox model With Current status data and tests of regression parameters in odds-rate models with right censored data. Optimal tests have not previously been Studied for these scenarios. We study the asymptotic distribution of the proposed tests Under the null, fixed Contiguous alternatives and random contiguous alternatives. We also propose a weighted bootstrap procedure for computing the critical values of the test statistics. The optimal tests perform well ill simulation Studies, where they may exhibit improved power over alternative tests.