Testing for Model Adequacy in Censored Location-Scale Families

• Activity Number: 403 - Selected Topics on Hypothesis Testing and Statistical Inference
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Sundarraman Subramanian*
• Companies: New Jersey Institute of Technology
• Keywords: Functional delta method ; Gaussian process ; Lagrange multiplier ; Nelson--Aalen estimator ; Kaplan--Meier quantile function ; Nonparametric maximum likelihood

Abstract

The empirical characteristic function as a tool to address function-based hypothesis testing for location-scale models works well for uncensored data. For censored location-scale models, when the two independent samples are each subjected to independent right censoring, a formal test of adequacy is lacking. A plug-in empirical likelihood approach is proposed, with minimum distance estimators of the location and scale parameters used as plug-in. A large-sample analysis of the plug-in empirical likelihood confirms the problem typical of such tests, which is that the test is not asymptotically distribution free. Hence for practical situations bootstrap is necessary for performing the test. Numerical studies are carried out to provide validation for the proposed testing method, and a real example is given to illustrate its practical use.