Robust confidence regions for the index and functional coefficients in the single-index varying coefficients regression model

A single-index varying coefficients regression model is considered, from which robust confidence regions/intervals of the regression parameters are derived. Considering the rank-based estimating equations, empirical likelihood objective functions of the index and functional coefficients objective functions are defined and their asymptotic properties are established under mild regularity conditions. The performance of the proposed approach is demonstrated via extensive Monte Carlo simulation experiments. The simulation results are compared with those obtained from a normal approximation alternative. Also the proposed method is compared with the least squares and least absolute deviations alternatives. Finally, a real data example is given to illustrate the method.