Penalized Spline Estimation for Single-Index Coefficient Models

• Activity Number: 378
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Zhou Wu*+ and Yan Yu
• Companies: University of Cincinnati and University of Cincinnati
• Keywords: dimension reduction ; nonparametric estimation ; nonlinear time series ; simulation ; varying-coefficient

Abstract

The single-index coefficient model, where the coefficients are functions of an index of a covariate vector, is a new powerful tool to model nonlinearity for time series. By reducing the covariate vector to an index, the single index coefficient model overcomes the "curse of dimensionality" that arises in nonparametric estimation. We propose a penalized spline approach to estimate coefficient functions of the single-index coefficient models. Each coefficient function is approximated by a spline with penalty terms to balance the goodness-of-fit of the model and the smoothness of coefficient functions. Implementation details are discussed. We show that the penalized least squares estimators are consistent and asymptotically normal under mild conditions. Moreover, our method has certain advantages over other methods. Different coefficient functions are allowed to have different smoothness with the aid of different penalty terms. The proposed p-spline approach is a global smoothing method which yields a parsimonious model and thus multistep forecasting based on the fitted model is straightforward. An application to GNP and simulated examples are presented to illustrate the approach.