Smoothing Spline ANOVA Models (Springer Series in Statistics), by Chong Gu
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Smoothing Spline ANOVA Models (Springer Series in Statistics), by Chong Gu
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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 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.
In this book, 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 lifetime 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 platform for statistical
computing and graphics. Suites of functions are embodied in the R
package gss, and are illustrated throughout the book using simulated
and real data examples.
This monograph will be useful as a reference work for researchers in
theoretical and applied statistics as well as for those in other
related disciplines. It can also be used as a text for graduate level
courses on the subject. Most of the materials are accessible to a
second year graduate student with a good training in calculus and
linear algebra and working knowledge in basic statistical inferences
such as linear models and maximum likelihood estimates.
Smoothing Spline ANOVA Models (Springer Series in Statistics), by Chong Gu- Published on: 2015-06-25
- Released on: 2015-06-25
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.07" w x 6.10" l, 1.38 pounds
- Binding: Paperback
- 433 pages
Review
“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 Back Cover
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.
In this book, 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 lifetime 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.
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.
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Most helpful customer reviews
30 of 30 people found the following review helpful. extension of the concept of smoothing splines to higher dimensional data By Michael R. Chernick 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.
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