P-splines regression smoothing and difference type of penalty

Authors:
I. Gijbels;A. Verhasselt
Affiliations:
Department of Mathematics and Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Leuven (Heverlee), Belgium 3001;Department of Mathematics and Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Leuven (Heverlee), Belgium 3001
Venue:
Statistics and Computing
Year:
2010

Citing 3
Cited 0

Matrix analysis

Matrix analysis
Curve and surface fitting with splines

Curve and surface fitting with splines
Fast Local Reconstruction Methods for Nonuniform Sampling in Shift-Invariant Spaces

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

P-splines regression provides a flexible smoothing tool. In this paper we consider difference type penalties in a context of nonparametric generalized linear models, and investigate the impact of the order of the differencing operator. Minimizing Akaike's information criterion we search for a possible best data-driven value of the differencing order. Theoretical derivations are established for the normal model and provide insights into a possible `optimal' choice of the differencing order and its interrelation with other parameters. Applications of the selection procedure to non-normal models, such as Poisson models, are given. Simulation studies investigate the performance of the selection procedure and we illustrate its use on real data examples.