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Smoothing Spline ANOVA Models

  • ChongĀ Gu

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Chong Gu
    Pages 1-20
  3. Chong Gu
    Pages 21-58
  4. Chong Gu
    Pages 111-148
  5. Chong Gu
    Pages 177-210
  6. Chong Gu
    Pages 211-230
  7. Chong Gu
    Pages 231-260
  8. Back Matter
    Pages 261-290

About this book

Introduction

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.

Keywords

ANOVA ANOVA models Likelihood Spline smoothing data analysis nonparametric smoothing smoothing methods

Authors and affiliations

  • ChongĀ Gu
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3683-0
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2966-2
  • Online ISBN 978-1-4757-3683-0
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site