Oracally Efficient Two-Step Estimation of Generalized Additive Model

Abstract

The generalized additive model (GAM) is a multivariate nonparametric regression tool for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions and the constant, which are oracally efficient under weak dependence. The SBK technique is both computationally expedient and theoretically reliable, thus usable for analyzing high-dimensional time series. Inference can be made on component functions based on asymptotic normality. Simulation evidence strongly corroborates the asymptotic theory. The method is applied to estimate insolvent probability and to obtain higher accuracy ratio than a previous study. Supplementary materials for this article are available online.

KEY WORDS:

• Bandwidths
• B-spline
• Knots
• Link function
• Mixing
• Nadaraya-Watson estimator

Acknowledgments

This work has been supported in part by National Science Foundation Awards DMS 0706518 and 1007594; funding from the National University of Singapore, the Jiangsu Specially-Appointed Professor Program, Jiangsu, China; and from Deutsche Forschungsgemeinschaft SFB 649 “Ökonomisches Risiko,” Humboldt-Universität zu Berlin. The very constructive comments of the Associate Editor and two Reviewers are gratefully acknowledged.