Curve fitting with splines is a fundamental problem in computer-aided design and engineering. However, how to choose the number of knots and how to place the knots in spline fitting remain a difficult issue. This paper presents a framework for computing knots (including the number and positions) in curve fitting based on a sparse optimizationmodel. The framework consists of two steps: first, fr...

Regression spline smoothing is a popular approach for conducting nonparametric regression. An important issue associated with it is the choice of a ‘‘theoretically best’’ set of knots. Different statistical model selection methods, such as Akaike’s information criterion and generalized cross-validation, have been applied to derive different ‘‘theoretically best’’ sets of knots. Typically these ...

Varying-coefficient models provide a flexible framework for semiand nonparametric generalized regression analysis. We present a fully Bayesian B-spline basis function approach with adaptive knot selection. For each of the unknown regression functions or varying coefficients, the number and location of knots and the B-spline coefficients are estimated simultaneously using reversible jump Markov ...

where Ni x ð Þ denotes the normalized cubic B-spline defined upon the knots i; iþ1; . . . ; iþ4. The total number n of these knots and their values 1; . . . ; n are chosen automatically by the routine. The knots 5; . . . ; n 4 are the interior knots; they divide the approximation interval x1; xm 1⁄2 into n 7 subintervals. The coefficients c1; c2; . . . ; cn 4 are then determined as the solution...

To compensate for lack of robustness in using regression splines via the least squares principle, a robust data smoothing procedure is proposed for obtaining a robust regression spline estimator of an unknown regression function, g 0 , of a one-dimensional measurement variable. This robust regression spline estimator is computed by using the usual M-type iteration procedures proposed for linear...