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Smoothing spline ANOVA models. 2nd ed. (English) Zbl 1269.62040
Springer Series in Statistics 297. New York, NY: Springer (ISBN 978-1-4614-5368-0/hbk; 978-1-4614-5369-7/ebook). xviii, 433 p. (2013).
[For the first edition from 2002 see Zbl 1051.62034.]
Publisher’s description: Nonparametric function estimation with stochastic data, otherwise known as smoothing, has been studied by several generations of statisticians. Assisted by the ample computing power in today’s servers, desktops, and laptops, smoothing methods have been finding their ways into everyday data analysis by practitioners. While scores of methods have proved successful for univariate smoothing, ones practical in multivariate settings number far less. Smoothing spline ANOVA models are a versatile family of smoothing methods derived through roughness penalties, that are suitable for both univariate and multivariate problems.
The author presents a treatise on penalty smoothing under a unified framework. Methods are developed for (i) regression with Gaussian and non-Gaussian responses as well as with censored life time data; (ii) density and conditional density estimation under a variety of sampling schemes; and (iii) hazard rate estimation with censored life time data and covariates. The unifying themes are the general penalized likelihood method and the construction of multivariate models with built-in ANOVA decompositions. Extensive discussions are devoted to model construction, smoothing parameter selection, computation, and asymptotic convergence.
Most of the computational and data analytical tools discussed in the book are implemented in R, an open-source clone of the popular S/S-PLUS language. Code for regression has been distributed in the R package gss freely available through the Internet on CRAN, the Comprehensive R Archive Network. The use of gss facilities is illustrated in the book through simulated and real data examples.

MSC:
62G08 Nonparametric regression and quantile regression
62J10 Analysis of variance and covariance (ANOVA)
62G07 Density estimation
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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