Efficient inferences on the varying-coefficient single-index model with empirical likelihood

The varying-coefficient single-index model (VCSIM) is a useful extension of the existing varying-coefficient model, the single-index model and partially linear single-index model. In this article, statistical inferences for the index parameter of interest for the VCSIM are investigated. By the empirical likelihood method proposed by Owen (2001), two new and simple estimating equations for the index parameter are constructed, then two efficient maximum empirical likelihood estimators (MELEs) of the index parameter are defined. Simulation results show that the proposed MELEs are asymptotically more efficient than existing estimators in terms of limiting variance. Based on the MELE, a new profile empirical likelihood for a single component of the parameter is defined. The resulting statistic is proved to follow a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed methodology.