Smoothing splines : methods and applications
著者
書誌事項
Smoothing splines : methods and applications
（Monographs on statistics and applied probability, 121）（A Chapman & Hall book）
CRC Press, Taylor & Francis Group, Informa business, c2011
- : hardback
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注記
Includes bibliographical references (p. 347-354) and indexes
内容説明・目次
内容説明
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.
目次
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.
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