Practical Smoothing The Joys of P-splines
Practical Smoothing: The Joys of P-splines by Paul H.C. Eilers is a comprehensive guide published by Cambridge University Press on March 18, 2021. This 208-page book presents P-splines, a versatile tool for smoothing that integrates regression on B-splines with discrete roughness penalties. The text explores the introduction of P-splines in 1996 and their application across various fields, emphasizing their ability to manage non-normal data through generalized linear models.
Readers will find detailed discussions on optimal smoothing techniques, including mixed model technology and Bayesian estimation, alongside classical methods like cross-validation and AIC. The book goes beyond basic smoothing, illustrating the use of P-splines for regression on signals, varying-coefficient models, and quantile smoothing. It also addresses penalties, which are essential for handling periodic data and shape constraints, and demonstrates how to extend these properties to multiple dimensions using tensor products of B-splines. An appendix provides a systematic comparison to other smoothing techniques, making this edition a valuable resource for those interested in mathematics, statistics, and signal processing.
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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.
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