Constrained nonparametric regression

In regression analysis, when no previous information about the statistical model is available, nonparametric estimation methods are very useful since their requirements about the specification of the model are very small (some conditions on continuity and derivability) . However if this previous information exists, we may like to have function estimates that firstly have the nice flexibility of nonparametric estimates, but secondly they are able to take into account this previous information. The constrained smoothing splines estimators that we introduce in this paper are one way to harmonize both requirements. In this paper we introduce the Constrained Smoothing Spline Estimators (CSSE) and we give some asymptotic properties.