Statistical Inference for Generalized Additive Partially Linear Model

Abstract

The class of Generalized Additive Models (GAMs) is a powerful tool which has been well studied. It helps to identify additive regression structure that can be determined even more sharply via test procedures when some component functions have a parametric form. Generalized Additive Partially Linear Models (GAPLMs) enjoy the simplicity of GLMs and the flexibility of GAMs because they combine both parametric and non-parametric components. We use the hybrid spline-back-fitted kernel estimation method, which combines the best features of both spline and kernel methods, to make fast, efficient and reliable estimation under an -mixing condition. In addition, simultaneous confidence corridors (SCCs) for testing overall trends and empirical likelihood confidence regions for parameters are provided under an independence condition. The asymptotic properties are obtained and simulation results support the theoretical properties. As an illustration, we use GAPLM methodology to improve the accuracy ratio of the default predictions for 19,610 German companies. The quantlet for this paper are available on https://github.com.

Keywords: B-Spline, Empirical Likelihood, Kernel Estimator, Link Function, Mixing

JEL Classification: C14, G33