Ruppert D., Wand M.P., Carroll R.J. Semiparametric Regression

Cambridge: Cambridge University Press, 2003. — 386 p. — (Cambridge Series in Statistical and Probabilistic Mathematics). — ISBN: 978-0-521-78050-6.Science abounds with problems where the data are noisy and the answer is not a straight line. Semiparametric regression analysis helps make sense of such data in application areas that include engineering, finance, medicine and public health. The book is geared towards researchers and professionals with little background in regression as well as statistically oriented scientists (biostatisticians, econometricians, quantitative social scientists, and epidemiologists) with knowledge of regression and the desire to begin using more flexible semiparametric models. Author resource page: http://www.stat.tamu.edu/~carroll/semiregbook/Assessing the Carcinogenicity of Phenolphthalein
Salinity and Fishing in North Carolina
Management of a Retirement Fund
Biomonitoring of Airborne Mercury
Term Structure of Interest Rates
Air Pollution and Mortality in Milan: The Harvesting Effect
Parametric RegressionLinear Regression Models
Regression Diagnostics
Inference
Parametric Additive Models
Model Selection
Polynomial Regression Models
Nonlinear Regression
Transformations in Regression
Bibliographic Notes
Summary of Formulas
Scatterplot SmoothingPreliminary Ideas
Practical Implementation
Automatic Knot Selection
Penalized Spline Regression
Quadratic Spline Bases
Other Spline Models and Bases
Other Penalties
General Definition of a Penalized Spline
Linear Smoothers
Error of a Smoother
Rank of a Smoother
Degrees of Freedom of a Smoother
Residual Degrees of Freedom
Other Approaches to Scatterplot Smoothing
Choosing a Scatterplot Smoother
Bibliographical Notes
Summary of Formulas
Mixed ModelsMixed Models
Prediction
The Linear Mixed Model (LMM)
Estimation and Prediction in LMM
Estimated BLUP (EBLUP)
Standard Error Estimation
Hypothesis Testing
Penalized Splines as BLUPs
Bibliographical Notes
Summary of Formulas
Automatic Scatterplot SmoothingThe Likelihood Approach
The Model Selection Approach
Caveats of Automatic Parameter Selection
Choosing the Knots and Basis Functions
Automatic Selection of the Number of Knots
Bibliographical Notes
Summary of Formulas
InferenceVariability Bands
Confidence and Prediction Intervals
Inference for Penalized Splines
Simultaneous Confidence Bands
Testing the Adequacy of Parametric Models
Testing for No Effect
Inference Using First Derivatives
Testing for Existence of a Feature
Bibliographical Notes
Summary of Formulas
Simple Semiparametric ModelsBeyond Scatterplot Smoothing
Semiparametric Binary Offset Model
Additivity and Interactions
General Parametric Component
Inference
Bibliographical Notes
Additive ModelsFitting an Additive Model
Degrees of Freedom
Smoothing Parameter Selection
Hypothesis Testing
Model Selection
Bibliographical Notes
Semiparametric Mixed ModelsAdditive Mixed Models
Subject-Specific Curves
Bibliographical Notes
Generalized Parametric RegressionBinary Response Data
Logistic Regression
Other Generalized Linear Models
Iteratively Reweighted Least Squares
Hat Matrix, Degrees of Freedom, and Standard Errors
Overdispersion and Variance Functions: Pseudolikelihood
Generalized Linear Mixed Models
Deviance
Technical Details
Bibliographical Notes
Generalized Additive ModelsGeneralized Scatterplot Smoothing
Generalized Additive Mixed Models
Degrees-of-Freedom Approximations
Automatic Smoothing Parameter Selection
Hypothesis Testing
Model Selection
Density Estimation
Bibliographical Notes
Interaction ModelsBinary-by-Continuous Interaction Models
Factor-by-Curve Interactions in Additive Models
Varying Coefficient Models
Continuous-by-Continuous Interactions
Bibliographical Notes
Bivariate SmoothingChoice of Bivariate Basis Functions
Kriging
General Radial Smoothing
Default Automatic Bivariate Smoother
Geoadditive Models
Additive Plus Interaction Models
Generalized Bivariate Smoothing
Appendix: Equivalence of BLUP using ZR and ZP
Bibliographical Notes
Variance Function EstimationFormulation
Application to the LIDAR Data
Quasilikelihood and Variance Functions
Bibliographical Notes
Measurement ErrorFormulation
The Expectation Maximization (EM) Algorithm
Simulated Example Revisited
Sensitivity Analysis Example
Bibliographical Notes
Bayesian Semiparametric RegressionGeneral Framework
Scatterplot Smoothing
Linear Mixed Models
Generalized Linear Mixed Models
Rao–Blackwellization
Bibliographical Notes
Spatially Adaptive SmoothingA Local Penalty Method
Completely Automatic Algorithm
Bayesian Inference
Simulations
LIDAR Example
Additive Models
Bibliographical Notes
Analyses
Cancer Rates on Cape Cod
Assessing the Carcinogenicity of Phenolphthalein
Salinity and Fishing in North Carolina
Management of a Retirement Fund
Biomonitoring of Airborne Mercury
Term Structure of Interest Rates
Air Pollution and Mortality in Milan: The Harvesting Effect
EpilogueMinimalist Statistics
Some Omitted Topics
Future Research
Technical ComplementsMatrix Definitions and Results
Linear Algebra
Probability Definitions and Results
Maximum Likelihood Estimation
Bibliographical Notes
Computational Issues
Fast Computation of Penalized Spline Smooths
Computation of Covariance Matrix Estimators
Software