Empirical Likelihood with Arbitrary Censored/Truncated Data by Constrained EM algorithm

• Activity Number: 158
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Mai Zhou*+ and Min Chen and Jingyu Luan
• Companies: University of Kentucky and University of Kentucky and University of Kentucky
• Keywords: maximization ; weighted hazard ; hazard constraints ; proportional hazard regression

Abstract

Empirical likelihood ratio method is a general nonparametric inference procedure with many desirable statistical properties. To apply this method, a crucial computational step is to find the nonparametric likelihood estimator (NPMLE) and the maximum log likelihood under some constraints, which was achieved by using the Lagrange Multiplier in a lot of cases. But if the data are arbitrary censored or truncated with a constraint on the hazard, the Lagrange Multiplier no longer works. Instead, the self-consistent/EM algorithm introduced by Turnbull (1976) can be modified to handle the computation here. We present a modified EM algorithm with a constraint on the hazard of the unknown distribution such that the maximum empirical likelihood can be calculated easily. Moreover, we extend the EM algorithm to the Cox proportional hazards regression model. The empirical likelihood under hypothesis of regression coefficient and constraint of hazard can be found so using of empirical likelihood ratio method to test the hypothesis of regression coefficient for arbitrary censored or truncated data becomes computationally viable.