Bias-Corrected Empirical Likelihood in Partially Linear Models with Right Censored Data

Abstract

A bias-corrected method is proposed to study partially linear models with right censored response data. The empirical likelihood ratios and estimators of the regression parameter and the baseline function are constructed, and their asymptotic distributions are given. The consistent estimators of asymptotic variances are also provided. The obtained results can be directly used to construct the confidence regions/intervals for the parameters of interest. Furthermore, we propose a method to construct simultaneous confidence band for the baseline function. Our approach is to directly calibrate the empirical log-likelihood ratio so that the resulting ratio is asymptotically Chi-squared. The undersmoothing of the baseline function is avoided, and the existing data-driven method is also valid for selecting an optimal bandwidth. Simulation studies are undertaken to compare the empirical likelihood with the normal approximation-based method. An example of an AIDS clinical trial data set is used to illustrate our approach.

Keywords

Empirical likelihood / Partially linear model / Censored data / Regression parameter / Confidence region. / 62N01 / 62N02

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Funding

National Natural Science Foundation of China(12471252, 11971001)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature

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