Research Methods and Statistics Arena

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• Price: $89.95 $80.96
• Hardback: 384 pages
• Published: June 2011
• ISBN: 978-1-4200775-5-1
• Publisher: Chapman and Hall/CRC

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A general class of powerful and flexible modeling techniques, spline smoothing has attracted a great deal of research attention in recent years and has been widely used in many application areas, from medicine to economics. Smoothing Splines: Methods and Applications covers basic smoothing spline models, including polynomial, periodic, spherical, thin-plate, L-, and partial splines, as well as more advanced models, such as smoothing spline ANOVA, extended and generalized smoothing spline ANOVA, vector spline, nonparametric nonlinear regression, semiparametric regression, and semiparametric mixed-effects models. It also presents methods for model selection and inference.

The book provides unified frameworks for estimation, inference, and software implementation by using the general forms of nonparametric/semiparametric, linear/nonlinear, and fixed/mixed smoothing spline models. The theory of reproducing kernel Hilbert space (RKHS) is used to present various smoothing spline models in a unified fashion. Although this approach can be technical and difficult, the author makes the advanced smoothing spline methodology based on RKHS accessible to practitioners and students. He offers a gentle introduction to RKHS, keeps theory at a minimum level, and explains how RKHS can be used to construct spline models.

Smoothing Splines offers a balanced mix of methodology, computation, implementation, software, and applications. It uses R to perform all data analyses and includes a host of real data examples from astronomy, economics, medicine, and meteorology. The codes for all examples, along with related developments, can be found on the book’s web page.

Table of Contents

Introduction

Parametric and Nonparametric Regression

Polynomial Splines

Scope of This Book

The assist Package

Smoothing Spline Regression

Reproducing Kernel Hilbert Space

Model Space for Polynomial Splines

General Smoothing Spline Regression Models

Penalized Least Squares Estimation

The ssr Function

Another Construction for Polynomial Splines

Periodic Splines

Thin-Plate Splines

Spherical Splines

Partial Splines

L-Splines

Smoothing Parameter Selection and Inference

Impact of the Smoothing Parameter

Trade-Offs

Unbiased Risk

Cross-Validation and Generalized Cross-Validation

Bayes and Linear Mixed-Effects Models

Generalized Maximum Likelihood

Comparison and Implementation

Confidence Intervals

Hypothesis Tests

Smoothing Spline ANOVA

Multiple Regression

Tensor Product Reproducing Kernel Hilbert Spaces

One-Way SS ANOVA Decomposition

Two-Way SS ANOVA Decomposition

General SS ANOVA Decomposition

SS ANOVA Models and Estimation

Selection of Smoothing Parameters

Confidence Intervals

Examples

Spline Smoothing with Heteroscedastic and/or Correlated Errors

Problems with Heteroscedasticity and Correlation

Extended SS ANOVA Models

Variance and Correlation Structures

Examples

Generalized Smoothing Spline ANOVA

Generalized SS ANOVA Models

Estimation and Inference

Wisconsin Epidemiological Study of Diabetic Retinopathy

Smoothing Spline Estimation of Variance Functions

Smoothing Spline Spectral Analysis

Smoothing Spline Nonlinear Regression

Motivation

Nonparametric Nonlinear Regression Models

Estimation with a Single Function

Estimation with Multiple Functions

The nnr Function

Examples

Semiparametric Regression

Motivation

Semiparametric Linear Regression Models

Semiparametric Nonlinear Regression Models

Examples

Semiparametric Mixed-Effects Models

Linear Mixed-Effects Models

Semiparametric Linear Mixed-Effects Models

Semiparametric Nonlinear Mixed-Effects Models

Examples

Appendix A: Data Sets

Appendix B: Codes for Fitting Strictly Increasing Functions

Appendix C: Codes for Term Structure of Interest Rates

References

Author Index

Subject Index

Author/Editor Biography

Yuedong Wang is a professor and the chair of the Department of Statistics and Applied Probability at the University of California–Santa Barbara. Dr. Wang is an elected fellow of the ASA and ISI, a fellow of the RSS, and a member of IMS, IBS, and ICSA. His research covers the development of statistical methodology and its applications.