On semiparametric regression with O'Sullivan penalised splines

TL;DR

This paper discusses the use of O'Sullivan penalised splines in semiparametric regression, highlighting their advantages over P-splines and providing practical implementation details for modern statistical software.

Contribution

It introduces exact expressions for the O'Sullivan penalty matrix and compares its boundary behavior to smoothing splines, enhancing understanding and application in regression models.

Findings

O'Sullivan penalised splines closely mimic natural boundary behavior.

Exact penalty matrix expressions are derived.

Implementation guidance for Matlab, R, and BUGS is provided.

Abstract

This is an expos\'e on the use of O'Sullivan penalised splines in contemporary semiparametric regression, including mixed model and Bayesian formulations. O'Sullivan penalised splines are similar to P-splines, but have an advantage of being a direct generalisation of smoothing splines. Exact expressions for the O'Sullivan penalty matrix are obtained. Comparisons between the two reveals that O'Sullivan penalised splines more closely mimic the natural boundary behaviour of smoothing splines. Implementation in modern computing environments such as Matlab, R and BUGS is discussed.