Smoothing with Curvature Constraints based on Boosting Techniques

In many applications it is known that the underlying smooth
function is constrained to have a specific form. In the present
paper, we propose an estimation method based on the regression
spline approach, which allows to include concavity or convexity
constraints in an appealing way. Instead of using linear or
quadratic programming routines, we handle the required inequality
constraints on basis coefficients by boosting techniques.
Therefore, recently developed componentwise boosting methods for
regression purposes are applied, which allow to control the
restrictions in each iteration. The proposed approach is compared
to several competitors in a simulation study. We also consider a
real world data set.