Empirical Likelihood Ratio for Differentiable Statistical Functional in Terms of Cumulative Hazard

• Activity Number: 28
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Zhiyuan Shen* and Mai Zhou
• Companies: University of Kentucky and University of Kentucky
• Keywords: Empirical likelihood ; Nelson-Aalen estimator ; Survival analysis ; Gini coefficient ; Statistical functional ; Hadamard differentiable

Abstract

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. It has been showed by Owen (1988,1990) and many others that empirical likelihood ratio (ELR) can be used to calculate confidence intervals. Owen showed that -2logELR converges to the chi-square distribution subject to a linear statistical functional in terms of distribution function. However, a generalization of Owen's setting to the right censored data is difficult since no explicit maximization can be obtained. Pan & Zhou (1998) extended the results to the right censored data using a linear statistical functional constraint in terms of cumulative hazard. In this paper, we would like to extend Pan & Zhou's results subject to a Hadamard differentiable non-linear statistical functional in terms of cumulative hazard. Stochastic process and martingale theories will be applied to prove the theorem. The confidence intervals are compared in a simulation to bootstrap and to some normal transformation methods. Real data analysis and simulations are demonstrated to illustrate our proposed theorem with an application to the Gini coefficient.