Empirical likelihood in some nonparametric and semiparametric models

In this very selective overview, we summarise the recent developments by our own and other, on the empirical likelihood in some nonparametric and semiparametric regression models. The models include the partially linear model, the single-index model, the partially linear singleindex model, the varying coefficient model, and so on. The focus of this overview is to expatiate the adjustment and "bias correction" methodologies when Wilks' phenomenon does not hold. The adjustment or bias correction can make the limiting distributions tractable such that they can be directly used to construct the confidence regions of parameters of interest without the assistance of Monte Carlo approximation.