Wang Smoothing Splines

Methods and Applications
Erscheinungsjahr 2011
ISBN: 978-1-4200-7756-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 384 Seiten

Reihe: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

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.

Zielgruppe

Researchers, practitioners, and graduate students in statistics and biostatistics; researchers in nonparametric regression, machine learning, and numerical analysis.

Autoren/Hrsg.

Wang, Yuedong

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Interdisziplinäres Wissenschaften Wissenschaften Interdisziplinär Naturwissenschaften, Technik, Medizin
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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

Über Autor(innen)

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.