Practical Smoothing : The Joys of P-splines

This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing.P-splines combine regression on B-splines with simple, discrete, roughness penalties.They were introduced by the authors in 1996 and have been used in many diverse applications.The regression basis makes it straightforward to handle non-normal data, like in generalized linear models.The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R.Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data.Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints.Combining penalties with tensor products of B-splines extends these attractive properties to multiple dimensions.An appendix offers a systematic comparison to other smoothers.