Paul H. C. Eilers

Practical Smoothing (eBook, ePUB)

The Joys of P-splines

• Format: ePub

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 18. März 2021
• Englisch
• ISBN-13: 9781108686884
• Artikelnr.: 62745394

Autorenporträt

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.

Inhaltsangabe

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.