Empirical likelihood for semiparametric varying-coefficient partially linear regression models

This paper is concerned with the estimating problem of the varying-coefficient partially linear regression model. We apply the empirical method to this semiparametric model. An empirical log-likelihood ratio for the parametric components, which are of primary interest, is proposed and the nonparametric version of the Wilk's theorem is derived. Thus, the confidence regions of the parametric components with asymptotically correct coverage probabilities can be constructed. Compared with those based on normal approximation, the confidence regions based on the empirical likelihood have two advantages: (1) they do not have the predetermined symmetry, which enables them to better correspond with the true shape of the underlying distribution; (2) they do not involve any asymptotic covariance matrix estimation and hence are robust against the heteroscedasticity. Some simulations and an application are conducted to illustrate the proposed method.