Documentation of the graphs.

Warning: copying and pasting the R code from these pdf documents can result in minor corruption of the R code.

When using the code in R, we suggest to go to the following zip archive where all of the R scripts are collected here.

• Chapter 1. Introduction
• Show the essence of P-splines
• Chapter 2. Bases, penalties, and likelihoods
• Polynomial fits (New York air quality data)
• Polynomial fits with differing support (Motorcycle data)
• B-splines in perspective
• Illustration of linear and quadratic B-spline bases
• B-spline fits having differing support (Motorcycle data)
• B-spline fits with differing number of segments (Motorcyle data)
• Illustration B-spline fits with varying basis size (Simulated data)
• B-spline fits with same basis having varying roughness
• First order difference penalty in action with various tuning
• Second order difference penalty in action with various tuning
• Illustration of interpolation and extrapolation by penalty order
• Smoothing of BMI and its derivative against age (Dutch boys data)
• Effective dimension with increased penalization
• Optimal P-spline fit with twice se bands (Motorcyle data)
• View of B-spline coefficients
• View of linear B-spline coefficients
• Equivalent kernels of Whittaker smoother with second order penalty
• Poisson smoothing with P-splines (Coal mining data)
• Binomial P-spline smoothing (Kyphosis data)
• Chapter 3. Optimal smoothing in action
• P-spline fits with various tuning (Motorcycle data)
• Optimal binomial smoothing (Kyphosis data)
• Optimal density estimation (Old Faithful geyser data)
• Density estimation with a sharp boundary (Suicide data)
• Tuning P-splines with mixed model lme and HFS algorithm (Motorcycle data)
• Slow convergence of Harville-Fellner-Schall algorithm
• Correcting low convergence of Schall algorithm with regula falsi
• Illustration of Bayesian P-splines
• Bayesian P-splines, based on example Jullion and Lambert
• Histogram smoothing with INLA
• Density estimation with digit preference (Old Faithful geyser data)
• Density estimation with digit preference using weights (Old Faithful geyser data)
• Fit overdispersed counts with different size bases (Greece deaths data)
• Quasi-likelihood fit of overdispersed (Greek death data)
• Optimal smoothing with L- and V-curve tuning (Wood surface data)
• L- and V-curves for optimal tuning (Wood surface data)
• Smoothing of BMI against age (Dutch boys data)
• Smoothing of BMI against square root of age (Dutch boys data)
• Chapter 4. Multidimensional smoothing
• GAM smoothing (Ethanol data)
• Image of GAM surface (Ethanol data)
• Illustration of varying slope (Hard disk price data)
• P-spline smooth of varying slope (Hard disk price data)
• Varying-coefficient components with Poisson response (Polio data)
• Tensor product surfaces, with various row and column tuning
• Impression of one B-spline tensor product and a tensor basis
• Tensor product P-spline fit (Ethanol data)
• Tensor product P-spline fit and extrapolation (Ethanol data)
• Smoothing ring image with array regression (Simulated data)
• Smoothing scattered data with array regression (Simulated data)
• Two-dimensional anisotropic density estimation (Old Faithful data)
• Two-dimensional isotropic density estimation (Old Faithful data)
• Effect of unequal segment numbers in 2D Bayesian smoothing (Simulated data)
• PS-ANOVA (Ethanol data)
• PS-ANOVA for precipitation anomaly data, with and without clipping (US precipitation data)
• Chapter 5. Smoothing of scale and shape
• Median smoothing with P-splines (Motorcycle data)
• Median P-spline smoothing with large basis (Motorcycle data)
• Median P-spline smoothing with double penalty (Motorcycle data)
• Quantile curves for body weight of 1000 boys (Dutch boys data)
• Quantile curves for body weight of 100 boys (Dutch boys data)
• Quantile sheet for body weight of 100 boys (Dutch boys data)
• Expectile smoothing of weight of 100 boys (Dutch boys data)
• Expectile smoothing of weight of 100 boys, CV tuned (Dutch boys data)
• Expectile smoothing of weight of 1000 boys (Dutch boys data)
• Expectile smoothing of weight of 1000 boys, Age 15, with density (Dutch boys data)
• Bundle model (LIDAR data)
• GAMLSS smoothing of weight of 100 boys (Dutch boys data)
• Box-Cox-Cole-Green smoothing of weight of 100 boys (Dutch boys data)
• GAMLSS smoothing for percentile curves (Motorcycle data)
• GAMLSS smoothing illustrating standard error bands (Motorcycle data)
• Baseline estimation by expectile smoothing (indiumoxide data)
• Chapter 6. Complex counts and composite links
• Composite link function density estimation (Lead data)
• Tuning of the composite link function density estimation (Lead data)
• Histogram of red blood cell distribution width (linear and log scales) (RDW data)
• Penalized composite link model to estimate density of log transformed data (RDW data)
• Density estimation from individual interval censored data (HIV data)
• Penalized CLM and negative binomial estimation (Complaints data)
• Chapter 7. Signal regression
• Original and differenced NIR spectra (Biscuit data)
• Penalized signal regression coefficient vectors (Biscuit data)
• Penalized signal regression optimally tuned with CV (Biscuit data)
• External prediction performance plot (Biscuit and Sugar data)
• Sample log-periodogram spectra (Phoneme data)
• Binomial signal regression optimally tuned (Phoneme data)
• ROC curve for Binomial signal regression (Phoneme data)
• Example of two-dimensonal image regressors (Sugar data)
• Image of optimal two-dimensional coefficient surface (Sugar data)
• Varying-coefficient and varying-link single-index fit (Sugar data)
• Chapter 8. Special subjects
• Proper and improper B-spline basis
• Harmonic penalty smoothing (Variable star data)
• Show effective kernels for the Whittaker smoother (Impulse)
• Circular B-spline basis
• Smoothing with and without a circular B-spline basis
• Smoothing of the circular frequency distribution of wind directions
• Whittaker trend and sinus, signal separation (ECG data)
• P-splines with PRIDE and Schall updates (Greece deaths data)
• Interpolation with double penalization using first and second orders
• Equivalent kernels for Whittaker smoother with double penalty
• Smoothing with the sum of absolute values of differences in penalty (Simulated data)
• Smoothing the L0 norm of absolute differences in penalty (Simulated data)
• Smoothing the sum of absolute differences in penalty (Chromosome data)
• Smoothing of BMI against age with zero slope constraint (Dutch boys data)
• Monotonic smoothing by asymmetric penalty (Hepatitis Bulgaria data)
• Non-monotone 2D smoothing (Simulated data)
• Monotone 2D smoothing with mixed model, updating lambda (Simulated data)
• Smoothing of swept sine, with a variable penalty (Simulated data)
• Adaptive smoothing with SOP (Indiumoxide data)
• Non-adaptive smoothing with SOP (Indiumoxide data)
• Survival analysis hazard smoothing, mixed model tuning (Ovarian cancer data)
• Smoothing of life table, monthly data (US Women cardiovascular data)
• Appendix C. Computational details
• Construction of linear B-splines from truncated power basis
• Construction of quadratic B-splines from truncated power basis
• Appendix E. Mixed model equations
• Density estimation with mixed model tuning (Old Faithful geyser data)
• Appendix F. Standard errors in detail
• Bayesian vs. sandwich covariance estimators (Simulated data)

Data

Some of the data sets we use come from R packages. Some others come from different sources. We have included them in our package and docmented their properties in the help files.