Bounded optimal knots for regression splines
Using a B-spline representation for splines with knots seen as free variables, the approximation to data by splines improves greatly. The main limitations are the presence of too many local optima in the univariate regression context, and it becomes even worse in multivariate additive modeling. When the number of knots is a priori fixed, we present a simple algorithm to select their location subject to box constraints for computing least-squares spline approximations. Despite its simplicity, or perhaps because of it, the method is comparable with other more sophisticated techniques and is very attractive for a small number of variables, as shown in the examples. In a complete algorithm, the BIC and AIC criteria are evaluated for choosing the number of knots as well as the degree of the splines.
additive models bic aic bound constrained optimization free knots selection surface estimation