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| View Larger Image | Smoothing Spline ANOVA Models
by Chong Gu
| | List Price: | $94.00 |  | | Available: | Usually ships in 24 hours | | | | | Sales Rank: | 1176750 | | Studio: | Springer | | | Binding: | Hardcover | | Number Of Pages: | 320 | | Publication Date: | January 08, 2002 | | Publisher: | Springer |
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EDITORIAL REVIEWS |
Product Description
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. |
CUSTOMER REVIEWS (Average Customer Rating: 5.0 based on 2 reviews)
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extension of the concept of smoothing splines to higher dimensional data 
The smoothing approach to density estimation and regression began with kernel methods in the 1950s and 1960s. For regression problems, smoothing splines were introduced using roughness penalties in the early pioneering work of Kimeldorf and Wahba 1970 & 1971 and the famous paper by Good and Gaskins in 1971. Since that time some excellent books have been written for univariate analysis based on this approach. The entertaining book by Green and Silverman (1994) comes to mind in particular.
Gu studied under Wahba at Wisconsin and has done research into this approach in multivariate contexts. This book presents results on smoothing splines using roughness penalties. It covers the gamut from fully parametric through semi-parametric to non-parametric solutions.
An interesting feature of the book is the decomposition of the resulting function into sums of functions that are analogous to the standard ANOVA decomposition in the general linear model. Chapter 1 is a clear introduction to all the key ideas in the book. It presents the cubic smoothing spline as the solution to a minimization problem with a peanlized least squares scoring function. Simple examples are used to illustrate the three key areas of application namely, (1) probability density estimation, (2) regression function estimation and (3) hazard function estimation. The ANOVA decomposition and several case studies are also presented in chapter 1. This provides the foundation for the rest of the book. The remaining chapters deal with these three estimation problems in more detail and provide software implementation and analysis of several case study examples.
This is very much an applications-oriented book, but the theory is not overlooked. Most of the relevant theory is presented in the last chapter, Chapter 8 "Asymptotic Convergence". The author goes to great pains to emphasize model construction, smoothing parameter selection, computational techniques (software and programming languages)and convergence results.
This book should be suitable to both practitioners and theorists.
January 22, 2008 | |
smoothing splines extended to mutivariate data
The smoothing approach to density estimation and regression began with kernel methods in the 1950s and 1960s. For regression problems, smoothing splines were introduced using roughness penalties in the early pioneering work of Kimeldorf and Wahba 1970 & 1971 and the famous paper by Good and Gaskins in 1971. Since that time some excellent books have been written for univariate analysis based on this approach. The entertaining book by Green and Silverman (1994) comes to mind in particular. Gu studied under Wahba at Wisconsin and has done research into this approach in multivariate contexts. This book presents results on smoothing splines using roughness penalties. It covers the gamut from fully parametric through semi-parametric to non-parametric solutions. An interesting feature of the book is the decomposition of the resulting function into sums of functions that are analogous to the standard ANOVA decomposition in the general linear model. Chapter 1 is a clear introduction to all the key ideas in the book. It presents the cubic smoothing spline as the solution to a minimization problem with a peanlized least squares scoring function. Simple examples are used to illustrate the three key areas of application namely, (1) probability density estimation, (2) regression function estimation and (3) hazard function estimation. The ANOVA decomposition and several case studies are also presented in chapter 1. This provides the foundation for the rest of the book. The remaining chapters deal with these three estimation problems in more detail and provide software implementation and analysis of several case study examples. This is very much an applications-oriented book, but the theory is not overlooked. Most of the relevant theory is presented in the last chapter, Chapter 8 "Asymptotic Convergence". The author goes to great pains to emphasize model construction, smoothing parameter selection, computational techniques (software and programming languages)and convergence results. This book should be suitable to both practitioners and theorists.
September 06, 2002 | |
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