Regression splines (parametric Smoothing splines (nonparametric) Basis functions One approach for extending the linear model is to represent z using a collection of basis functions: M fe)=∑Bmtim(d) m=1 Because the basis functions [hm}are prespecified and the model is linear in these new variables,ordinary least squares approaches for model fitting and inference can be employed o This idea is probably not new to you,as transformations and expansions using polynomial bases are common Patrick Breheny STA 621:Nonparametric StatisticsIntroduction Regression splines (parametric) Smoothing splines (nonparametric) Basis functions One approach for extending the linear model is to represent x using a collection of basis functions: f(x) = X M m=1 βmhm(x) Because the basis functions {hm} are prespecified and the model is linear in these new variables, ordinary least squares approaches for model fitting and inference can be employed This idea is probably not new to you, as transformations and expansions using polynomial bases are common Patrick Breheny STA 621: Nonparametric Statistics