Asymptotics for penalized splines in generalized additive models

TL;DR

This paper develops asymptotic theory for penalized spline estimators in generalized additive models, including bias, variance, and normality, and extends the results to penalized quasi-likelihood fits in mixed models.

Contribution

It provides the first comprehensive asymptotic analysis of penalized spline estimators in generalized additive models and related mixed models.

Findings

Asymptotic bias and variance formulas derived

Establishment of asymptotic normality of estimators

Extension to penalized quasi-likelihood in mixed models

Abstract

This paper discusses asymptotic theory for penalized spline estimators in generalized additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the penalized spline estimators proposed by Marx and Eilers (1998). Furthermore, the asymptotics for the penalized quasi likelihood fit in mixed models are also discussed.