Statistical inference for generalized additive partially linear models

Abstract

The Generalized Additive Model (GAM) is a powerful tool and has been well studied. This model class helps to identify additive regression structure. Via available test procedures one may identify the regression structure even sharper if some component functions have parametric form. The Generalized Additive Partially Linear Models (GAPLM) enjoy the simplicity of the GLM and the flexibility of the GAM because they combine both parametric and nonparametric components. We use the hybrid spline-backfitted kernel estimation method, which combines the best features of both spline and kernel methods for making fast, efficient and reliable estimation under α-mixing condition. In addition, simultaneous confidence corridors (SCCs) for testing overall trends and empirical likelihood confidence region for parameters are provided under independent condition. The asymptotic properties are obtained and simulation results support the theoretical properties. For the application, we use the GAPLM to improve the accuracy ratio of the default predictions for 19610 German companies. The quantlet for this paper are available on https://github.com.

Asymptotic theory for extreme value generalized additive models

“…for some constant C * > 0. From the condition of ε N that nε 2 N /{K log(N )} → ∞, we have N exp[−C * nε 2 N ] → 0, which implies (16). We next assume (S2).…”