Spline Smoothing with an Estimated Order Parameter

Asymptotic Properties of Smoothing Parameter Selection in Spline Smoothing

The asymptotic properties of smoothing parameter estimates for smoothing splines are developed. We consider a variety of estimates including Generalized Cross Validation, Generalized Maximum Likelihood, and more generally Type II ML estimates and the properties of the marginal posterior mode. Under the usual Sobolov space frequentist assumptions on the function to be estimated , consistency and...

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...

Smoothing by Spline Functions

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...

Monotone B-spline Smoothing

Estimation of growth curves or item response curves often involves monotone data smoothing. Methods that have been studied in the literature tend to be either less exible or more diicult to compute when constraints such as monotonicity are incorporated. Built upon the ideas of Ramsay (1988) and Koenker, Ng and Portnoy (1994), we propose monotone B-spline smoothing based on L 1 optimization. It ...