Practical Smoothing: The Joys of P-splines

Copyright
Dedication
Contents
Preface
1 Introduction
2 Bases, Penalties, and Likelihoods
	2.1 Linear and Polynomial Regression
	2.2 B-splines
	2.3 Penalized Least Squares
	2.4 Interpolation and Extrapolation
	2.5 Derivatives
	2.6 The Effective Dimension
	2.7 Standard Errors
	2.8 Heavy Smoothing and Polynomial Limits
	2.9 P-splines as a Parametric Model
	2.10 Whittaker: P-splines without B-splines
	2.11 Equivalent Kernels
	2.12 Smoothing of a Non-normal Response
		2.12.1 Poisson Smoothing
		2.12.2 Binomial Smoothing
		2.12.3 GLM Effective Dimension and Standard Errors
	2.13 Notes and Details
3 Optimal Smoothing in Action
	3.1 Cross-Validation
	3.2 Akaike’s Information Criterion
	3.3 Density Estimation
	3.4 Mixed Models
	3.5 Bayesian P-splines
	3.6 Dangers of Automatic Smoothing
	3.7 L- and V-curves
	3.8 Transformation of the Independent Variable
	3.9 Notes and Details
4 Multidimensional Smoothing
	4.1 Generalized Additive Models
	4.2 Varying Coefficient Models
	4.3 Tensor Product Models
	4.4 Tensor Product Bases
	4.5 Two-Dimensional Penalties
	4.6 Interpolation and Extrapolation
	4.7 Smoothing on Large Grids
	4.8 Generalized Two-Dimensional Smoothing
	4.9 Optimal Two-Dimensional Smoothing
	4.10 Issues with Isotropic Smoothing
	4.11 Higher Dimensions
	4.12 Nested Bases and PS-ANOVA
	4.13 Notes and Details
5 Smoothing of Scale and Shape
	5.1 Quantile Smoothing
	5.2 Expectile Smoothing
	5.3 Models for Shape and Scale Parameters
	5.4 Baseline Estimation
	5.5 Notes and Details
6 Complex Counts and Composite Links
	6.1 Histograms with Wide Bins
	6.2 Histograms and Scale Transformation
	6.3 Individual Censoring
	6.4 Latent Mixtures
	6.5 Notes and Details
7 Signal Regression
	7.1 A Chemical Calibration Problem
	7.2 Extensions to the Generalized Linear Model
	7.3 Multidimensional Signal Regression
	7.4 Further Extensions
	7.5 Notes and Details
8 Special Subjects
	8.1 The Proper B-spline Basis
	8.2 Harmonic Smoothing
	8.3 Circular Smoothing
	8.4 Signal Separation with Penalties
	8.5 Double Penalties
	8.6 Piecewise Constant Smoothing
	8.7 Shape Constraints
	8.8 Variable and Adaptive Penalties
	8.9 Survival Analysis and Mortality Modeling
	8.10 Notes and Details
Appendix A P-splines for the Impatient
Appendix B P-splines and Competitors
Appendix C Computational Details
Appendix D Array Algorithms
Appendix E Mixed Model Equations
Appendix F Standard Errors in Detail
Appendix G The Website
References
Index