Practical Smoothing

The Joys of P-Splines
Erscheinungsjahr 2021
ISBN: 978-1-108-48295-0
Verlag: Cambridge University Press

Buch, Englisch, 200 Seiten, Format (B × H): 154 mm x 232 mm, Gewicht: 452 g

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.

Autoren/Hrsg.

Eilers, Paul H C

Marx, Brian D

Fachgebiete

• Mathematik | Informatik EDV | Informatik EDV & Informatik Allgemein
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning

Inhaltsverzeichnis

1. Introduction; 2. Bases, penalties, and likelihoods; 3. Optimal smoothing in action; 4. Multidimensional smoothing; 5. Smoothing of scale and shape; 6. Complex counts and composite links; 7. Signal regression; 8. Special subjects; A. P-splines for the impatient; B. P-splines and competitors; C. Computational details; D. Array algorithms; E. Mixed model equations; F. Standard errors in detail; G. The website.

Über Autor(innen)

Marx, Brian D
Brian D. Marx is Professor in the Department of Experimental Statistics at Louisiana State University. He received his Ph.D. in statistics. His main research interests include smoothing, ill-conditioned regression problems, and high-dimensional chemometric applications, and he has numerous publications on these topics. He is currently serving as coordinating editor for the journal Statistical Modelling. He is coauthor of two books and is a Fellow of the American Statistical Association.

Eilers, Paul H C
Paul H. C. Eilers is Professor Emeritus of Genetical Statistics at the Erasmus University Medical Center Rotterdam. He received his Ph.D. in biostatistics. His research interests include high-throughput genomic data analysis, chemometrics, smoothing, longitudinal data analysis, survival analysis, and statistical computing. He has published extensively on these subjects.