Simple and Multiple Regression Splines with Bounded Optimal Knots

Using a B-spline representation for splines, knots seen as free variables, the approximation to data by splines improve greatly. The damage due to the presence of a lot of local optima is very important in the univariate regression context, and things are getting worse in multivariate additive modeling. We present a new algorithm to select knots submitted to constraints for computing least squares spline approximations.