Empirical likelihood-based inference in varying-coefficient single-index models

This article deals with statistical inferences based on varying-coefficient parts in varying-coefficient single-index models (VCSIM). To improve the accuracy of the normal approximation-based confidence regions/intervals, an estimated empirical likelihood-based statistic is proposed. The resulting statistic is shown to be asymptotically chi-squared distributed. The construction of the empirical likelihood-based confidence regions of some varying-coefficient components in VCSIM is considered. In addition, the pointwise confidence intervals for a single function of the varying-coefficient parts are constructed. A simulation study is carried out to compare our results with several existing methods.