Schimek M.G. Smoothing and Regression: Approaches, Computation, and Application

Hoboken: Wiley, 2000. — 648 p.A comprehensive introduction to a wide variety of univariate and multivariate smoothing techniques for regressionSmoothing and Regression: Approaches, Computation, and Application bridges the many gaps that exist among competing univariate and multivariate smoothing techniques. It introduces, describes, and in some cases compares a large number of the latest and most advanced techniques for regression modeling. Unlike many other volumes on this topic, which are highly technical and specialized, this book discusses all methods in light of both computational efficiency and their applicability for real data analysis.Using examples of applications from the biosciences, environmental sciences, engineering, and economics, as well as medical research and marketing, this volume addresses the theory, computation, and application of each approach. A number of the techniques discussed, such as smoothing under shape restrictions or of dependent data, are presented for the first time in book form. Special features of this book include:* Comprehensive coverage of smoothing and regression with software hints and applications from a wide variety of disciplines* A unified, easy-to-follow format* Contributions from more than 25 leading researchers from around the world* More than 150 illustrations also covering new graphical techniques important for exploratory data analysis and visualization of high-dimensional problems* Extensive end-of-chapter referencesFor professionals and aspiring professionals in statistics, applied mathematics, computer science, and econometrics, as well as for researchers in the applied and social sciences, Smoothing and Regression is a unique and important new resource destined to become one the most frequently consulted references in the field.ForewordGeneral Form of the Estimator
The Linear Smoothing Spline
Large-Sample Efficiency
Bayesian Motivation
Extensions and ImplementationsIntroduction and Some Definitions
Interpretation of the Smoothing Parameter
Quantifying the Complexity of a Smoothing Spline
Estimation of σ
Determination of λThe Nadaraya–Watson Kernel Regression Estimate
Pointwise Bias Properties of the Nadaraya–Watson Estimate
Pointwise Variance Properties of the Nadaraya–Watson Estimate
Trade-off Between Bias and Variance: The Mean Squared Error
Global Results: Mean Integrated Squared Error Properties
L∞ Convergence Properties of the NadarayaW–atson Estimate
Complementary BibliographyNonparametric Variance Estimators
Bandwidth Choice for Kernel Regression EstimatorsDescription of the Main Methods
A Comparative View
Examples
Software HintsApproaches for a Known Autocorrelation Function
Approaches for an Unknown Autocorrelation Function
A Bayesian Approach to Smoothing Dependent Data
Applications of Smoothing Dependent DataWavelet Expansions
The Discrete Wavelet Transform in S
Wavelet Shrinkage
Estimators for Data With Correlated Noise
Implementation of the Wavelet Transform
How to Obtain and Install the Wavelet SoftwareSmoothing Contingency Tables
Smoothing Approaches to Categorical RegressionProperties of Local Polynomial Fitting
Choice of Bandwidth
Choice of the Degree
Local Modeling
Some More ApplicationsThe Additive Model
Generalized Additive Models
Alternating Conditional Expectations Additivity, and Variance Stabilization
Smoothing Parameter and Bandwidth Determination
Model Diagnostics
New DevelopmentsSmoothing Splines as Bayes Estimates
ANOVA Decomposition on Product Domains
Tensor Product Splines
Computation
Bayesian Confidence Intervals
Software
Cosine Diagnostics
Partial Splines
Thin-Plate Splines
Non-Gaussian RegressionMultidimensional Smoothing with Kernels
Semiparametric Generalized Regression Models
Practical Application and Software HintsThin-Plate Splines
Spatial-Process Estimates
Ridge-Regression Estimates and Shrinkage
A Response-Surface Example
Predicting Ambient Ozone
Future DirectionsThe Idea of Bootstrap
Bootstrap in Nonparametric Regression
Bootstrap Confidence Intervals and Bands
Bootstrap-Bandwidth Choice
Bootstrap Tests in Nonparametrics
Bootstrap Inference on the Shape of a Curve
ExtensionsData-Point Visualization
Functional Visualization in One and Two Variables
Averaged Shifted Histograms
Functional Visualization in Three Variables and Beyond
Visualization of Regression FunctionsThe Basic PPR Algorithm
Quality of Approximation
Number of Terms to Choose
Interpretable PPR
Convergence Rates
Modifications
PPR and Neural Networks
Optimization Methods for PPR and Neural Networks
The Implementation of PPR in S-PLUS R, and Xplore
An ExampleThe Idea
Statistical Properties
The Unknown Dimensionality
Slicing Strategies
Implementation
Modifications
An ExampleLinear Dynamic Models and Optimal Smoothing for Time Series Data
Non-Gaussian Observation Models
Generalized Additive and Varying Coefficient Models
ConclusionsBayesian Model and Subset Selection
Bivariate Surface Estimation
Robust Surface Estimation
Surface Estimation for Time Series Data
Alternative Bases and Model Mixing