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Nonparametric function estimation with stochastic data, otherwise known as smoothing, has been studied by several generations of statisticians. Assisted by the recent availability of ample desktop and laptop computing power, smoothing methods are now 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. In this book, the author presents a comprehensive treatment of 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.
Introduction.- Model Construction.- Regression with Gaussian Type Responses.- More Splines.- Regression with Exponential Families.- Probability Density Estimation.- Hazard Rate Estimation.- Asymptotic Convergence.
From the reviews: TECHNOMETRICS "The book is well organized in eight clearly written chapters, each of which includes a closing section with useful bibliographic notes and problems for the reader![This book] is recommended for a range of audiences. Researchers of smoothing methods with roughness penalties will likely appreciate this book!Sophisticated practitioners may look to the book's examples for modeling ideas and guidance. Instructors of advanced graduate-level statistical modeling courses may want to consider the book as a textbook. Also, instructors in a RKHS-oriented functional analysis course may find the book a valuable reference for applications." SHORT BOOK REVIEWS "This is the only book available now written exclusively on the method of smoothing spline ANOVA, a newly-developed and broadly applicable approach to nonparametric functional estimation problems. The author is one of the few main contributors to the development of this field." "This book presents a comprehensive treatment of penalized likelihood smoothing under a unified framework. A broad variety of models with ANOVA decompositions is covered for regression, density and hazard rate estimation. ! I particularly like the case studies a lot, which allow the reader to see the methods work in practice ! . I consider the book to be a good reference for researchers interested in spline smoothing in a general context as it ! gives many bibliographic notes for further reading." (R. Fried, Metrika, February, 2004) "The book is well organized in eight clearly written chapters, each of which includes a closing section with useful bibliographic notes and problems for the reader. ! Smoothing Spline ANOVA Models is recommended for a range of audiences. Researchers of smoothing methods with roughness penalties will likely appreciate this book. ! Instructors of advanced graduate-level statistical modeling courses may want to consider the book as a textbook. Also, instructors in a RKHS-oriented functional analysis course may find the book a valuable reference for applications." (Michael Frey, Technometrics, Vol. 45 (3), August, 2003) "This book is a systematic presentation of function estimation on generic domains using the penalized likelihood method. ! The bibliographic notes given at the end of each chapter present a good overview of the material contained therein. Most of the computational work is implemented in software which is user-friendly and is available free from the various web sites." (Girdhar G. Agarwal, Mathematical Reviews, 2003 d)