Censored Empirical Likelihood with Overdetermined Hazard-Type Constraints

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yanling Hu*+ and Mai Zhou
• Companies: University of Kentucky and University of Kentucky
• Keywords: Over-determined constraints ; Censored data ; Asymptotic chi-square distribution ; Martingale theory

Abstract

Qin and Lawless (1994) studied the empirical likelihood method with estimating equations. They obtained very nice asymptotic properties especially when the number of estimation equations are larger than the number of parameters (over determined case). We study here a parallel setup to Qin and Lawless but uses a hazard-type empirical likelihood function and hazard-type estimating equations. The advantage of using hazard is that censored data can be handled easily. We obtained similar asymptotic results for the maximum empirical likelihood estimator and the empirical likelihood ratio test, also for the over determined case. Two examples are provided to demonstrate the potential application of the result.