Statistical Inference for Generalized Additive Partially Linear Model

TL;DR

This paper introduces a hybrid spline-backfitted kernel estimation method for generalized additive partially linear models, providing efficient estimation, confidence corridors, and empirical likelihood regions, with applications to credit default prediction.

Contribution

It develops a novel hybrid estimation approach for GAPLMs, combining spline and kernel methods, with theoretical properties and practical applications demonstrated.

Findings

The method achieves fast and reliable estimation under alpha-mixing conditions.

Simulations confirm the theoretical asymptotic properties.

Application improves default prediction accuracy for German companies.

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 alpha-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 quantlets for this paper are available on https://github.com.