Semiparametric regression 1st Edition by David Ruppert, MP Wand, RJ Carroll ISBN 0521785162 9780521785167

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ISBN 10: 0521785162 
ISBN 13: 9780521785167
Author: David Ruppert, MP Wand, RJ Carroll

Semiparametric regression 1st Table of contents:

1 Introduction
1.1 Assessing the Carcinogenicity of Phenolphthalein
1.2 Salinity and Fishing in North Carolina
1.3 Management of a Retirement Fund
1.4 Biomonitoring of Airborne Mercury
1.5 Term Structure of Interest Rates
1.6 Air Pollution and Mortality in Milan: The Harvesting Effect
2 Parametric Regression
2.1 Introduction
2.2 Linear Regression Models
2.2.1 General Linear Model
2.3 Regression Diagnostics
2.3.1 Influence Diagnostics
2.3.2 Autocorrelation
2.3.3 The Building Blocks of Regression Diagnostics
2.4 Inference
2.4.1 Confidence and Prediction Intervals
2.4.2 Inference about the Regression Coefficients
2.4.3 t-Statistics and p-Values
2.4.4 Inference about the Mean Response
2.4.5 Inference about New Observations
2.4.6 Estimation of Sigma
2.4.7 Extra Sums of Squares and Hypothesis Testing
2.5 Parametric Additive Models
2.5.1 Displaying Additive Fits
2. 5.1.1 Vertical Alignment
2.5.1.2 Variability Bands
2.5.1.3 Partial Residuals
2.5.1.4 Derivative Plots
2.5.2 Degrees of Freedom
2.6 Model Selection
2.7 Polynomial Regression Models
2.8 Nonlinear Regression
2.9 Transformations in Regression
2.9.1 LIDAR Monitoring of Air Pollutants
2.10 Bibliographic Notes
2.11 Summary of Formulas
3 Scatterplot Smoothing
3.1 Introduction
3.2 Preliminary Ideas
3.3 Practical Implementation
3.4 Automatic Knot Selection
3.5 Penalized Spline Regression
3.6 Quadratic Spline Bases
3.7 Other Spline Models and Bases
3.7.1 B-Splines
3.7.2 Natural Cubic Splines
3.7.3 Radial Basis Functions
3.8 Other Penalties
3.9 General Definition of a Penalized Spline
3.10 Linear Smoothers
3.11 Error of a Smoother
3.12 Rank of a Smoother
3.13 Degrees of Freedom of a Smoother
3.14 Residual Degrees of Freedom
3.15 Other Approaches to Scatterplot Smoothing
3.15.1 Local Polynomial Fitting
3.15.2 Series-Based Smoothers
3.16 Choosing a Scatterplot Smoother
3.17 Bibliographic Notes
3.18 Summary of Formulas
4 Mixed Models
4.1 Introduction
4.2 Mixed Models
4.2.1 Degrees-of-Freedom Interpretation
4.3 Prediction
4.3.1 Best Linear Prediction (BLP)
4.3.2 Application to Pig Weight Example
4.4 The Linear Mixed Model (LMM)
4.5 Estimation and Prediction in LMM
4.5.1 Estimation of Fixed Effects
4.5.2 Prediction of Random Effects
4.5.3 Best Linear Unbiased Prediction (BLUP)
4.5.4 Estimation of Covariance Matrices
4.6 Estimated BLUP (EBLUP)
4.7 Standard Error Estimation
4.7.1 Summary of Fit to Pig Weights
4.8 Hypothesis Testing
4.8.1 Normal Theory Tests
4.8.2 Likelihood Ratio Tests
4.8.3 Restricted Likelihood Ratio Tests
4.9 Penalized Splines as BLUPs
4.10 Bibliographical Notes
4.11 Summary of Formulas
5 Automatic Scatterplot Smoothing
5.1 Introduction
5.2 The Likelihood Approach
5.3 The Model Selection Approach
5.3.1 Cross-Validation (CV)
5. 3.1.1 Computation of CV
5.3.2 Generalized Cross-Validation (GCV)
5.3.2.1 Age and Income Data
5.3.3 Mallows’s C Criterion
5.3.3.1 Estimation of Sigma
5.3.3.2 Relationship between GCV and C
5.3.4 Other Model Selection Criteria
5.4 Caveats of Automatic Parameter Selection
5.5 Choosing the Knots and Basis Functions
5.5.1 Varying the Number of Knots
5.5.2 Varying the Degree of the Regression Spline
5.5.3 Default Choices for Knot Locations
5.6 Automatic Selection of the Number of Knots
5.6.1 Myopic Algorithm
5.6.2 Full-Search Algorithm
5.6.3 A Simulation Study
5.6.4 Fossil Data
5.7 Bibliographical Notes
5.8 Summary of Formulas
6 Inference
6.1 Introduction
6.2 Variability Bands
6.3 Confidence and Prediction Intervals
6.4 Inference for Penalized Splines
6.5 Simultaneous Confidence Bands
6.6 Testing the Adequacy of Parametric Models
6.6.1 Restricted Likelihood Ratio Tests
6. 6.1.1 Null Distribution of the Likelihood Ratio
6.6.2 F-Test Approach
6.6.3 Simulation for p-Values
6.7 Testing for No Effect
6.7.1 F-Test for No Effect
6.8 Inference Using First Derivatives
6.8.1 Derivative Estimation via Penalized Splines
6.8.2 Choosing the Smoothing Parameter
6.8.3 LIDAR Data
6.9 Testing for Existence of a Feature
6.10 Bibliographical Notes
6.11 Summary of Formulas
7 Simple Semiparametric Models
7.1 Introduction
7.2 Beyond Scatterplot Smoothing
7.3 Semiparametric Binary Offset Model
7.4 Additivity and Interactions
7.5 General Parametric Component
7.6 Inference
7.6.1 Hypothesis Tests
7.7 Bibliographical Notes
8 Additive Models
8.1 Introduction
8.2 Fitting an Additive Model
8.3 Degrees of Freedom
8.4 Smoothing Parameter Selection
8.4.1 Upper Cape Cod Birthweight Data
8.5 Hypothesis Testing
8.5.1 Likelihood Ratio Tests
8.5.2 F-tests
8.6 Model Selection
8.6.1 All-Subsets Algorithms
8.6.2 Stepwise Algorithms
8.6.3 MCMC Model Selection Algorithms
8.7 Bibliographical Notes
9 Semiparametric Mixed Models
9.1 Introduction
9.2 Additive Mixed Models
9.2.1 Additive Model Extension
9.2.2 Serially Correlated Errors
9.3 Subject-Specific Curves
9.4 Bibliographical Notes
10 Generalized Parametric Regression
10.1 Introduction
10.2 Binary Response Data
10.3 Logistic Regression
10.4 Other Generalized Linear Models
10.4.1 Poisson Regression and Overdispersion
10.4.2 The Gaussian GLM: A Model for Symmetrically Distributed and Homoscedastic Responses
10.4.3 The Gamma GLM: A Model with a Constant Coefficient of Variation
10.5 Iteratively Reweighted Least Squares
10.6 Hat Matrix, Degrees of Freedom, and Standard Errors
10.7 Overdispersion and Variance Functions: Pseudolikelihood
10.7.1 Quasilikelihood and Overdispersion Parameters
10.8 Generalized Linear Mixed Models
10.8.1 Estimation of Model Parameters
10.8.2 Penalized Quasilikelihood (PQL)
10.8.3 GLIMMIX
10.8.4 Bias Correction to PQL
10.8.5 Fitting via Expectation Maximization
10.8.6 Bayesian Fitting via Markov Chain Monte Carlo
10.8.7 Prediction of Random Effects
10.8.8 Standard Error Estimation
10.8.9 Bias Adjustment
10.9 Deviance
10.10 Technical Details
10.10.1 Fitting a Logistic Regression
10.10.2 Standard Error Estimation in Logistic Regression
10.10. 3 The Hat Matrix and Degrees of Freedom
10.10.4 Derivation of PQL
10.11 Bibliographical Notes
11 Generalized Additive Models
11.1 Introduction
11.2 Generalized Scatterplot Smoothing
11.2.1 Application to Wage–Union Data
11.3 Generalized Additive Mixed Models
11.4 Degrees-of-Freedom Approximations
11.5 Automatic Smoothing Parameter Selection
11.6 Hypothesis Testing
11.7 Model Selection
11.8 Density Estimation
11.9 Bibliographical Notes
12 Interaction Models
12.1 Introduction
12.2 Binary-by-Continuous Interaction Models
12.2.1 Testing for Additivity
12.3 Factor-by-Curve Interactions in Additive Models
12.3.1 Modularity of Spline Models
12.3.2 Example: Ragweed Pollen Revisited
12.3.3 Discrete-by-Continuous Interactions
12.3.4 Interactions in Additive Models
12.3.5 Generalized Additive Models with Interactions
12.3.6 Pollen Data
12.4 Varying Coefficient Models
12.5 Continuous-by-Continuous Interactions
12.6 Bibliographical Notes
13 Bivariate Smoothing
13.1 Introduction
13.2 Choice of Bivariate Basis Functions
13.3 Kriging
13.3.1 The Kriging Algorithm
13.4 General Radial Smoothing
13.4.1 Generalized Covariance Functions
13.4.2 Positive Definitization
13.4.3 Proper Covariance Matrices
13.4.4 Low-Rank Radial Smoothers
13.4.5 Higher-Dimensional Radial Smoothers
13.4.6 Choice of Knots
13.4.7 Degrees of Freedom
13.5 Default Automatic Bivariate Smoother
13.6 Geoadditive Models
13.7 Additive Plus Interaction Models
13.8 Generalized Bivariate Smoothing
13.9 Appendix: Equivalence of BLUP using Z and Z
13.10 Bibliographical Notes
14 Variance Function Estimation
14.1 Introduction
14.2 Formulation
14.3 Application to the LIDAR Data
14.4 Quasilikelihood and Variance Functions
14.5 Bibliographical Notes
15 Measurement Error
15.1 Introduction
15.2 Formulation
15.3 The Expectation Maximization (EM) Algorithm
15.4 Simulated Example Revisited
15.5 Sensitivity Analysis Example
15.6 Bibliographical Notes
16 Bayesian Semiparametric Regression
16.1 Introduction
16.2 General Framework
16.2.1 Markov Chain Monte Carlo
16.2.2 Credible Sets
16.3 Scatterplot Smoothing
16.3.1 Application to LIDAR Data
16.3.2 Application to Age and Income Data
16.4 Linear Mixed Models
16.5 Generalized Linear Mixed Models
16.5.1 Probit Mixed Models
16.5.1.1 Union and Wages Data Revisited
16.6 Rao–Blackwellization
16.7 Bibliographical Notes
17 Spatially Adaptive Smoothing
17.1 Introduction
17.2 A Local Penalty Method
17.3 Completely Automatic Algorithm
17.4 Bayesian Inference
17.5 Simulations
17.5.1 Effects of the Tuning Parameters
17.5.2 The Automatic Algorithms
17.5.3 Bayesian Inference
17.6 LIDAR Example
17.7 Additive Models
17.7.1 An Algorithm for Additive Models
17.7.2 Simulations of an Additive Model
17.8 Bibliographical Notes
18 Analyses
18.1 Cancer Rates on Cape Cod
18.2 Assessing the Carcinogenicity of Phenolphthalein
18.3 Salinity and Fishing in North Carolina
18.4 Management of a Retirement Fund
18.5 Biomonitoring of Airborne Mercury
18.6 Term Structure of Interest Rates
18.7 Air Pollution and Mortality in Milan: The Harvesting Effect
19 Epilogue
19.1 Introduction
19.2 Minimalist Statistics
19.3 Some Omitted Topics
19.3.1 Robustness
19.3.2 Quantile Regression
19.3.3 Nonquadratic Penalties
19.3.4 Highly Adaptive Smoothing
19.3.5 Missing Data
19.3.6 Functional Data Analysis
19.3.7 Survival Analysis
19.3.8 Single-Index Models
19.3.9 Diagnostics
19.3.10 Statistical Learning
19.3.11 Constrained Smoothing
19.3.12 Smoothing Geographical Count Data
19.3.13 Other Topics
19.4 Future Research
A Technical Complements
A.1 Introduction
A.2 Matrix Definitions and Results
A.2.1 Trace
A.2.2 Eigenvalues and Eigenvectors
A.2.3 Rank
A.2.4 Diagonalization
A.2.5 Elementwise Function Notation
A.2.6 Definiteness
A.2.7 Triangular Matrices
A.2.8 Cholesky Decomposition
A.2.9 QR Decomposition
A.2.10 Singular Value Decomposition
A.2.11 Matrix Square Root
A.2.12 Derivative Vector and Hessian Matrix
A.3 Linear Algebra
A.3.1 Vectors and Vector Spaces
A.3.2 Linear Combination and Span
A.3.3 Linear Dependence and Independence
A.3.4 Bases
A.4 Probability Definitions and Results
A.4.1 Mean of a Random Vector
A.4.2 Covariance Matrix of a Random Vector
A.4.3 Conditional Distribution, Mean, and Covariance Matrix
A.4.4 Bayes Theorem
A.4.5 Results Concerning Mean Vector and Covariance Matrix
A.4.6 Multivariate Normal Distribution
A.5 Maximum Likelihood Estimation
A.6 Bibliographical Notes
B Computational Issues
B.1 Fast Computation of Penalized Spline Smooths
B.1.1 Demmler–Reinsch Orthogonalization
B.1.1.1 Justification of Algorithm A.1
B.1.1.2 S-PLUS Implementation of Algorithm A.1
B.1.1.3 MATLAB Implementation of Algorithm A.1
B.1.1.4 Multipredictor Extension
B.1.2 QR Decomposition
B.1.2.1 Justification of Algorithm A.2
B.2 Computation of Covariance Matrix Estimators
B.3 Software
B.3.1 Smoothing Software
B.3.1.1 S-PLUS Functions
B.3.1.2 S-PLUS and R Modules
B.3.1.3 The SemiPar Module
B.3.1.4 SAS Procedures
B.3.2 S-PLUS Mixed Model Functions
B.3.3 SAS Mixed Model Procedures
B.3.4 WinBugs
B.3.4.1 Logistic Semiparametric Models
B.3.4.2 Binomial Responses
B.3.4.3 Poisson Semiparametric Models
B.3.4.4 Gaussian Semiparametric Models
B.3.4.5 Other Models

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Tags: David Ruppert, MP Wand, RJ Carroll, Semiparametric regression