Synopses & Reviews
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.
Synopsis
Driven by many sophisticated applications and fuelled by modern computing power, many powerful and flexible nonparametric and semiparametric modeling techniques have been developed to relax traditional parametric models and exploit possible hidden structure. As one of the most popular nonparametric techniques, the smoothing spline model has attracted a great deal of research attention in recent years.
This book covers basic nonparametric spline models, such as polynomial spline, periodic spline, thin-plate spline, L- spline, partial spline, and smoothing spline ANOVA for both Gaussian data and data from exponential families. It also presents smoothing spline models with unequal variance and correlated random errors as well as advanced models, including semiparametric linear and nonlinear mixed-effects models and nonparametric and semiparametric nonlinear regression models. In addition, the author describes vector spline models for multivariate observations and functional linear models.