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Practical Smoothing - The Joys of P-splines (Hardcover)
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Practical Smoothing - The Joys of P-splines (Hardcover)
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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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