Smoothing Spline ANOVA Models / Edition 1

by Chong Gu

Overview

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.

Product Details

ISBN-13:	9781441929662
Publisher:	Springer-Verlag New York, LLC
Publication date:	12/10/2010
Series:	Springer Series in Statistics
Edition description:	Softcover reprint of hardcover 1st ed. 2002
Pages:	304
Product dimensions:	6.10(w) x 9.10(h) x 0.80(d)

About the Author

Chong Gu received his Ph.D. from University of Wisconsin-Madison in 1989, and has been on the faculty in Department of Statistics, Purdue University since 1990. At various times during his career, he has held visiting appointments at University of British Columbia, University of Michigan, and National Institute of Statistical Sciences.

Table of Contents

Introduction.- Model Construction.- Regression with Gaussian Type Responses.- More Splines.- Regression with Exponential Families.- Probability Density Estimation.- Hazard Rate Estimation.- Asymptotic Convergence.

Editorial Reviews

The purpose of the book is to comprehensively present smoothing and penalized splines from the point of view of reproducing kernel Hilbert spaces (RKHS). … the book makes a valuable contribution to the literature on smoothing and penalized splines, especially for more mathematically oriented researchers.” (W. John Braun, Technometrics, Vol. 56 (4), November, 2014)

From the Publisher