Twenty years of P-splines Articles uri icon

publication date

  • October 2015

start page

  • 149

end page

  • 189


  • 2


  • 39

International Standard Serial Number (ISSN)

  • 1696-2281

Electronic International Standard Serial Number (EISSN)

  • 2013-8830


  • 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 difference 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 analysis have been established. We give an overview of many of the central developments during the first two decades of P-splines.


  • Statistics


  • 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