Constrained smoothing and interpolating spline surfaces using normalized uniform B-splines

On Mixed Interpolating-Smoothing Splines and the ν-Spline

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...

Interpolating and Approximating Moving Frames Using B-splines

The representation of moving geometry entities is an important issue in the fields of CAD/CAM and robotics motion design. We present a method to interpolate the moving frame homogeneously using B-splines. By analysing the matrix representation of the moving frames, a simplified optimization functional is derived and a recursive iteration method is presented for approximating orthogonal frames a...

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 ...

Uniform Error Bounds for Smoothing Splines

Almost sure bounds are established for the uniform error of smoothing splines in nonparametric regression with random designs. Some kernel-like properties of the Green’s function for an appropriate boundary value problem are needed to reduce the problem to that for kernel-like regression estimators. Then, results of Einmahl and Mason (2005) imply the required bounds, uniformly in the smoothing ...