GAM
- smoothing bases
- natural cubic splines are smoothest interpolators
- cubic smoothing splines
- cubic regression splines
- cyclic cubic regression spline
- p-splines
- thin plate regression splines
- tensor products smooths
- polynomial spline
- cubic spline
- regression spline
- on knots evenly spaced or with quantiles
- penalizing to avoid overfitting
- for \(\lambda\) known, it is still a augmented linear model
- select \(\lambda\) with ordinary cross validation
- computational and invariante advante og generalized cross validation
- Implementation
- initialize lambda
- given lambda, obtain beta
- compute gcv, and interate with previous step
- Identifiability, constrain one the rest of intercept parameters to zero.