Asymptotics for penalised splines in generalised additive models

Abstract

This paper discusses asymptotic theory for penalised spline estimators in generalised additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the ridge-corrected penalised spline estimator. Furthermore, the asymptotics for the penalised quasi-likelihood fit in mixed models are also discussed.

Keywords:

• asymptotic normality
• B-spline
• generalised additive model
• mixed model
• penalised spline

Acknowledgements

The authors are grateful to the Editor, Professor Irène Gijbels and two anonymous referees for their valuable comments and suggestions, which led to improvements in the paper. The research of the second author was partially supported by KAKENHI 23500350.