Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models

Empirical-likelihood-based inference for the nonparametric parts in semiparametric varying-coefficient partially linear (SVCPL) models is investigated. An empirical log-likelihood approach to construct the confidence regions/intervals of the nonparametric parts is developed. An estimated empirical likelihood ratio is proved to be asymptotically standard χ2χ2-limit. A simulation study indicates that, compared with a normal approximation-based approach and the bootstrap method, the proposed method described herein works better in terms of coverage probabilities and average areas/widths of confidence regions/bands. An application to a real data set is illustrated.