Splines and Smoothing

Wed, 11 Nov 2026 14:00:00 +1100

A straight line is often the wrong shape for \(E[Y \mid X = x]\). This page collects the ways of letting the regression function \(f\) bend in one predictor while the fit stays an ordinary least-squares problem (or a ridge-like one): polynomials, step functions, regression splines, natural splines, penalised splines and smoothing splines. All of them are linear smoothers, \(\hat{\mathbf y} = \mathbf S \mathbf y\) with \(\mathbf S\) depending only on the \(x\)’s, and that single fact carries the degrees-of-freedom bookkeeping and the cross-validation shortcut. 𐃏

Basis-Functions on Aayush Bajaj's Augmenting Infrastructure

Splines and Smoothing