Abstract: For the past two decades, the single-index model, a special case of projection pursuit regression, has proven to be an efficient way of coping with the high-dimensional problem in nonparametric regression. In this paper, based on a weakly dependent sample, we investigate a robust single-index model, where the single-index is identified by the best approximation to the multivariate prediction function of the response variable, regardless of whether the prediction function is a genuine single-index function. A polynomial spline estimator is proposed for the single-index coefficients, and is shown to be root-n consistent and asymptotically normal. An iterative optimization routine is used that is sufficiently fast for the user to analyze large data sets of high dimension within seconds. Simulation experiments have provided strong evidence corroborating the asymptotic theory. Application of the proposed procedure to the river flow data of Iceland has yielded superior out-of-sample rolling forecasts.
Key words and phrases: B-spline, geometric mixing, knots, nonparametric regression, root-n rate, strong consistency.