- 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.
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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.

(source: Nielsen Book Data)