Twenty years of P-splines (invited article)

• Paul H.C. Eilers ^[2] ; Brian D. Marx ^[1] ; Maria Durbán ^[3]
  1. [1] Louisiana State University

     Louisiana State University

     Estados Unidos

     
  2. [2] Erasmus University Medical Centre
  3. [3] Universidad Carlos III. Departamento de Estadística

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• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 39, Nº. 2, 2015, págs. 149-186
• Idioma: inglés
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• Resumen

  • 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.