Wang Y. Smoothing Splines. Methods and Applications

CRC Press, 2011. — 380 p. — (Monographs on Statistics and Applied Probability 121). — ISBN: 978-1-4200-7756-8.Statistical analysis often involves building mathematical models that examine the relationship between dependent and independent variables. This book is about a general class of powerful and flexible modeling techniques, namely, spline smoothing.Research on smoothing spline models has attracted a great deal of attention in recent years, and the methodology has been widely used in many areas. This book provides an introduction to some basic smoothing spline models, including polynomial, periodic, spherical, thin-plate, L-, and partial splines, as well as an overview of more advanced models, including smoothing spline ANOVA, extended and generalized smoothing spline ANOVA, vector spline, nonparametric nonlinear regression, semiparametric regression, and semiparametric mixed-effects models. Methods for model selection and inference are also presented.The general forms of nonparametric/semiparametric linear/nonlinear fixed/mixed smoothing spline models in this book provide unified frameworks for estimation, inference, and software implementation. This book draws on the theory of reproducing kernel Hilbert space (RKHS) to present various smoothing spline models in a unified fashion. On the other hand, the subject of smoothing spline in the context of RKHS and regularization is often regarded as technical and difficult. One of my main goals is to make the advanced smoothing spline methodology based on RKHS more accessible to practitioners and students. With this in mind, the book focuses on methodology, computation, implementation, software, and application. It provides a gentle introduction to the RKHS, keeps theory at the minimum level, and provides details on how the RKHS can be used to construct spline models.User-friendly software is key to the routine use of any statistical method. The assist library in R implements methods presented in this book for fitting various nonparametric/semiparametric linear/nonlinear fixed/mixed smoothing spline models. Rather than formal analysis, these examples are intended to illustrate the power and versatility of the spline smoothing methodology. All data analyses are performed in R, and most of them use functions in the assist library.This book is intended for those wanting to learn about smoothing splines. It can be a reference book for statisticians and scientists who need advanced and flexible modeling techniques. It can also serve as a text for an advanced-level graduate course on the subject. In fact, topics in Chapters 1–4 were covered in a quarter class at the University of California — Santa Barbara, and the University of Science and Technology of China.Smoothing Spline Regression
Smoothing Parameter Selection and Inference
Smoothing Spline ANOVA
Spline Smoothing with Heteroscedastic and/or Correlated Errors
Generalized Smoothing Spline ANOVA
Smoothing Spline Nonlinear Regression
Semiparametric Regression
Semiparametric Mixed-Effects Models
A: Data Sets
B: Codes for Fitting Strictly Increasing Functions
C: Codes for Term Structure of Interest Rates