Analysis of Deviance for Hypothesis Testing in Generalized Partially Linear Models

TL;DR

This paper introduces nonparametric deviance analysis tools for generalized partially linear models, enabling hypothesis testing of nonparametric terms with chi-square tests, supported by simulations and real data application.

Contribution

It develops new nonparametric deviance analysis methods for generalized partially linear models, including chi-square tests, extending existing techniques and providing practical tools.

Findings

Chi-square tests effectively assess nonparametric term significance

Simulation studies compare proposed tests with penalized splines methods

Application to real economic data demonstrates practical utility

Abstract

In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance, which admit an additivity property that reduces to analysis of variance decompositions in the Gaussian case. Chi-square tests based on integrated likelihood functions are proposed to formally test whether the nonparametric term is significant. Simulation results are shown to illustrate the proposed chi-square tests and to compare them with an existing procedure based on penalized splines. The methodology is applied to German Bundesbank Federal Reserve data.