Empirical Likelihood in Partial Linear Error-in-Covariable Model with Censored Data

Abstract

This article considers the estimation issue in a partial linear model with error-in-covariable and censored response. The proposed estimator of the parametric function in the model has been proved to be asymptotically normal in the literature. In this article, we shall apply the empirical likelihood method into the censored partial linear model with error-in-covariable. In particular, an empirical log-likelihood ratio of β is proposed and shown to have a limiting distribution of a weighted sum of independent chi-square distribution, which can be used to construct an approximate confidence region for β. Some simulation studies are conducted to compare the empirical likelihood method and normal approximation-based method, which indicate that the former is better.

Key Words:

• Asymptotic normally
• Empirical
• Partial linear model with error-in-covariable