Regression splines(parametric) Smoothing splines (nonparametric) Basis functions for piecewise continuous models o It can be easily checked that these basis functions lead to a composite function f(z)that: Is everywhere continuous Is linear everywhere except the knots Has a different slope for each region Also,note that the degrees of freedom add up:3 regions x 2 degrees of freedom in each region-2 constraints =4 basis functions Patrick Breheny STA 621:Nonparametric StatisticsIntroduction Regression splines (parametric) Smoothing splines (nonparametric) Basis functions for piecewise continuous models It can be easily checked that these basis functions lead to a composite function f(x) that: Is everywhere continuous Is linear everywhere except the knots Has a different slope for each region Also, note that the degrees of freedom add up: 3 regions × 2 degrees of freedom in each region - 2 constraints = 4 basis functions Patrick Breheny STA 621: Nonparametric Statistics