I congratulate Chen and Van Keilegom for writing this extensive and useful review on empirical likelihood methods in many contexts of regression. I am also very grateful to the editors of Test for the opportunity to take part in this discussion. This invited paper starts with parametric regression, where the main concepts and advantages of empirical likelihood are clearly shown. Later on, nonparametric and semiparametric models, missing and censored data, and a goodness-of-fit test are treated with the most recent and relevant proposals in each framework. For this reason, this review is very useful both as an introduction to the empirical likelihood methods for regression and as an updating on recent developments. My first specific comment is about the possibility of using empirical likelihood to obtain confidence bands in nonparametric regression. I did not find this in the literature, so I wonder whether it has been done, and if not, how it could be done. In parametric regression with censored response (Sect. 6.1), this review presents a very interesting option between a censored data likelihood and a complete data likelihood. The main details of Zhou and Li (2008) are given, where a censored data likelihood is used for mean regression. The proposal by Qin and Tsao (2003) is also presented, where a complete data likelihood is used in the context of median regression. Finally, the advantage of censored data likelihood is stressed, in the sense that it does not require the estimation of unknown functions. This is very appealing, so I looked for other frameworks where a censored data likelihood could be applied. I think it is the case of Stute (1999), where a weighted
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