Empirical likelihood in a partially linear single-index model with censored response data

An empirical likelihood (EL) approach for a partial linear single-index model with censored response data is studied. A bias-corrected EL ratio is proposed, and the asymptotic chi-squared distribution of this ratio is obtained. The result can be directly used to construct the confidence regions of the regression parameters. The estimators of regression parameters and link function are constructed, and their asymptotic distributions are obtained. Also, a confidence band of the link function is constructed. The proposed method has two main features: The first feature is that the EL ratio is calibrated directly from within, instead of multiplying an adjustment factor by an EL ratio, which reflects the nature of EL. The second feature is avoiding undersmoothing of nonparametric functions, thus ensuring that the $\sqrt{n}$-consistency of the parameter estimator. As a byproduct, the EL and estimation of a single-index model with censored response data are studied. The performance of the bias-corrected EL is evaluated by the simulation studies. The proposed method is illustrated with an example of a real data analysis.