Comments on: A review on empirical likelihood methods for regression

Abstract

Professors Chen and Keilegom have given a comprehensive and timely review on recent developments of empirical likelihood methods for regression. They have covered a wide array of topics including parametric regression, nonparametric regression, semiparametric regression, missing data, censored data regression, and goodness-of-fit tests. Our discussion will focus only on Sect. 6.1 regarding semiparametric linear regression for randomly right-censored data. Here we prefer to use the term “semiparametric regression” instead of “parametric regression” for Sect. 6.1 since the probabilistic model includes the completely unknown error distribution as a non-parametric component. Professors Chen and Keilegom have discussed two popular empirical likelihood (EL) methods, a synthetic data EL method (cf. Qin and Jing 2001, Li and Wang 2003, and Qin and Tsao 2003), and a censored data EL method (cf. Zhou and Li 2008) for semiparametric linear regression with censored data. These two methods are based on the approaches of Koul, Susarla, and Van Ryzin (KSV) (1981) and Buckley and James (1979), respectively. Their properties have also been contrasted nicely in the paper. In particular, the synthetic data EL method requires a restrictive assumption that the censoring time C is independent of both the covariate X and the survival time Y, whereas the censored data EL method of Zhou and Li (2008) only assumes that the censoring time C is conditionally independent of Y given X. Below we present some numerical examples to illustrate that the synthetic data approach is very sensitive to the independence assumption of C and X. Hence caution should be exercised when using the synthetic data approach in practice. For simplicity, we only consider point estimation in the following discussion.