  In this paper, we develop statistical inference techniques for the unknown
coefficient functions and single-index parameters in single-index
varying-coefficient models. We first estimate the nonparametric component via
the local linear fitting, then construct an estimated empirical likelihood
ratio function and hence obtain a maximum empirical likelihood estimator for
the parametric component. Our estimator for parametric component is
asymptotically efficient, and the estimator of nonparametric component has an
optimal convergence rate. Our results provide ways to construct the confidence
region for the involved unknown parameter. We also develop an adjusted
empirical likelihood ratio for constructing the confidence regions of
parameters of interest. A simulation study is conducted to evaluate the finite
sample behaviors of the proposed methods.
