Empirical likelihood and estimation in varying coefficient models with right censored data

In this paper, the empirical likelihood and estimations problems in varying coefficient models with right censored data are investigated by using a bias correction method. Naive and residual-adjusted empirical likelihood ratios and estimators of the coefficient functions are constructed, their asymptotic distributions are obtained, and a consistent estimator of the asymptotic variance is given. The obtained results can be directly used to construct the confidence regions of the coefficient functions. Furthermore, a new method for constructing pointwise confidence intervals and simultaneous confidence bands for each coefficient function is also proposed. The proposed method is to directly calibrate the empirical log-likelihood ratio so that the obtained ratio is asymptotically chi-squared. Undersmoothing of each coefficient function is avoided, and existing data-driven methods can also effectively select the optimal bandwidth. Simulation study is performed to compare the empirical likelihood with the normal approximation-based method. An example of real data is used to illustrate our approach.