Chapter 2: Bases, penalties and likelihoods

Equivalent kernels of Whittaker smoother with second order penalty

Equivalent kernels of Whittaker smoother with second order penalty

New York air quality data polynomial fits (air quality data)

New York air quality data polynomial fits (air quality data)

P-spline fit with twice se bands, optimal on CV (Motorcyle data)

P-spline fit with twice se bands, optimal on CV (Motorcyle data)

Illustration of linear and quadratic B-spline bases

Illustration of linear and quadratic B-spline bases

Compare a small and large number of B-splines (Motorcycle data)

Compare a small and large number of B-splines (Motorcycle data)

B-spline fits with same basis having varying roughness

B-spline fits with same basis having varying roughness

Second order difference penalty in action with various tuning

Second order difference penalty in action with various tuning

First order difference penalty in action with various tuning

First order difference penalty in action with various tuning

B-spline fits having differing support (Motorcycle data)

B-spline fits having differing support (Motorcycle data)

Smoothing of BMI and its derivative against age (boys7482 data)

Smoothing of BMI and its derivative against age (boys7482 data)

Polynomial fits with differing support (Motorcycle data)

Polynomial fits with differing support (Motorcycle data)

B-splines in perspective

B-splines in perspective

Effective dimension with increased penalization

Effective dimension with increased penalization

Illustration of interpolation and extrapolation by penalty order

Illustration of interpolation and extrapolation by penalty order

View of linear B-spline coefficients

View of linear B-spline coefficients

View of B-spline coefficients

View of B-spline coefficients

Illustration B-splines differing number of segments (simulated data)

Illustration B-splines differing number of segments (simulated data)