Smoothing Splines: Methods and Applications

ISBN-13: 9781032477626 / Angielski / Miękka / 2023 / 394 str.

Yuedong Wang

Opis

With many real-world examples, this book shows how to apply the powerful methods of smoothing splines in practice. It covers basic smoothing spline models as well as more advanced models, such as spline smoothing with correlated random errors. It also presents methods for model selection and inference. The author makes the advanced smoothing spl

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.

Spis treści

Introduction. 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. Appendices. References. Indices.

O autorze

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.