Smoothing Splines: Methods and Applications

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