Spline smoothing with model-based penalties

Model diagnostics for smoothing spline ANOVA models

The author proposes some simple diagnostics for the assessment of the necessity of selected model terms in smoothing spline ANOVA models; the elimination of practically insignificant terms generally enhances the interpretability of the estimates, and sometimes may also have inferential implications. The diagnostics are derived from Kullback-Leibler geometry, and are illustrated in the settings ...

Smoothing by Spline Functions

Smoothing an arc spline

Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route p...

Penalized Regression with Model-Based Penalties

Nonparametric regression techniques such as spline smoothing and local tting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function based on observations ti; Yi is the minimizer of P(Yi (ti))2 + R ( 00)2. Since R ( 00)2 is zero when is a line, the cubic smoothing spline estimate favors the parametric model (t) = 0+ 1t: Here we conside...

Spline Smoothing on Surfaces

We present a method for estimating functions on topologically and/or geometrically complex surfaces from possibly noisy observations. Our approach is an extension of spline smoothing, using a Þnite element method. The paper has a substantial tutorial component: we start by reviewing smoothness measures for functions deÞned on surfaces, simplicial surfaces and differentiable structures on such s...