Analysis of Deviance for Hypothesis Testing in Generalized Partially Linear Models

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.

KEY WORDS:

• ANOVA decomposition
• Integrated likelihood
• Local polynomial regression.

ACKNOWLEDGMENTS

We thank the editor, associate editor, and two anonymous referees for their constructive comments and suggestions. The work was conceived during the visit of the second author to the Humboldt-Universität zu Berlin supported by CRC 649 “Economic Risk.” The support is greatly appreciated. The first author was partially supported by SKBI School of Business, Singapore Management University, the second author (corresponding author) was partially supported by the Ministry of Science and Technology NSC 101-2118-M-007-002-MY2 in Taiwan, and both authors were partially supported by CRC 649 “Economic Risk.” The authors wish to thank Mr. Leslie Udvarhelyi who assisted in the proof-reading of the article.