Publication: Twenty years of P-splines
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Publication date
2015-10-01
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Tutors
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Statistical Institute of Catalonia (IDESCAT)
Abstract
P-splines first appeared in the limelight twenty years ago. Since then they have become popular
in applications and in theoretical work. The combination of a rich B-spline basis and a simple dif-
ference penalty lends itself well to a variety of generalizations, because it is based on regression.
In effect, P-splines allow the building of a “backbone” for the “mixing and matching” of a variety
of additive smooth structure components, while inviting all sorts of extensions: varying-coefficient
effects, signal (functional) regressors, two-dimensional surfaces, non-normal responses, quantile
(expectile) modelling, among others. Strong connections with mixed models and Bayesian analy-
sis have been established. We give an overview of many of the central developments during the
first two decades of P-splines.
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Keywords
B-Splines, Penalty, Additive model, Mixed model, Multidimensional smoothing, Structured additive regression, Varying coefficient models, Single index models, Penalized signal regression, Generalized linear models, Composite link model, Space time data, Semiparametric regression, Maximum likelihood
Bibliographic citation
Eilers, P. H. C., Marx, B. D., & Durbán, M. (2015). Twenty years of P-splines (invited article) [JD]. SORT. Statistics and Operations Research Transactions, 39, 149–186.