Flexible modelling using basis expansions (Chapter 5) Linear ...

Smoothing splines◮ How many parameters have been fit?◮ It can be shown that the solution to the smoothing splineproblem gives fitted values of the formŷ = S λ y◮ By analogy with ordinary regression, define the effectivedegrees of freedom (EDF) astrace S λ◮ Reminder: ridge regressionmin Σ N i=1 (y i − β 0 − β 1 x i1 − · · · − β p x ip ) 2 + λΣ pβj=1 β2 j⇐⇒ minβΣ N i=1 (y i − β 0 − β 1 x i1 − · · · − β p x ip ) 2 s.t. Σ p j=1 β2 j ≤ shas solutionŷ ridge = X(X T X + λI) −1 X T y: , 12