Smoothing Spline ANOVA Models

Updated to include the latest computational methods, this second edition explains how to use the 'gss' R package and features expanded empirical studies, a reorganized content, and a further new appendix analyzing new and controversial topics in smoothing.

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 accessibleto 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.

Covers latest research of smoothing methods in data analysis Second edition is updated with latest computational methods, including the uses ofthe R package gss Empirical studies are expanded, reorganized, and mostly rerun using the latest software Two new appendices are also added, outlining the overall design of the R package gss and coverage of new and controversial topics on smoothing methods Includes supplementary material: sn.pub/extras

Autorentext

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.

Klappentext

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.

Inhalt
Introduction.- Model Construction.- Regression with Gaussian-Type Responses.- More Splines.- Regression and Exponential Families.- Regression with Correlated Responses.- Probability Density Estimation.- Hazard Rate Estimation.- Asymptotic Convergence.- Penalized Pseudo Likelihood.