Empirical likelihood and estimation in single-index varying-coefficient models with censored data

In this paper, we study the empirical likelihood and estimation of parameters of interest in single-index varying coefficient models with right censored data. A bias-corrected empirical log-likelihood ratio statistic for the regression parameter is proposed. It is shown the the statistic is asymptotically standard chi-squared, and thus the confidence region of the regression parameter is constructed. The estimators for both the regression parameter and the coefficient functions are constructed, their asymptotic distributions are obtained, and the consistent estimators for the asymptotic variances are given. The obtained results can be directly used to construct the confidence regions of the regression parameter and the pointwise confidence intervals of the coefficient functions. Our approach is to directly calibrate the empirical log-likelihood ratio, so that the resulting ratio is asymptotically chi-squared, undersmoothing of the coefficient functions is avoided, and the existing data-driven methods can effectively select the optimal bandwidth. The finite-sample behavior of the new methods is evaluated through simulation studies, and the application to a real data is illustrated.