Spline estimation of density and its score function

This work introduces a new density estimation method based integrating an estimated score function. The score function is itself estimated by the minimization of a L 2 square distance with an added roughness penalty, resulting in a spline function. A computational algorithm is developed for this purpose. The asymptotic behavior of the estimators is studied under the light of a kernel representation. An approximate cross validation criterion for the choice of the smoothing parameter, is derived. Some simulation results are given illustrating the good performance of the method.