Abstract
In this paper, we study the robust estimation and empirical likelihood for the regression parameter in generalized linear models with right censored data. A robust estimating equation is proposed to estimate the regression parameter, and the resulting estimator has consistent and asymptotic normality. A bias-corrected empirical log-likelihood ratio statistic of the regression parameter is constructed, and it is shown that the statistic converges weakly to a standard χ2 distribution. The result can be directly used to construct the confidence region of regression parameter. We use the bias correction method to directly calibrate the empirical log-likelihood ratio, which does not need to be multiplied by an adjustment factor. We also propose a method for selecting the tuning parameters in the loss function. Simulation studies show that the estimator of the regression parameter is robust and the bias-corrected empirical likelihood is better than the normal approximation method. An example of a real dataset from Alzheimer's disease studies shows that the proposed method can be applied in practical problems.