Density estimation over complicated domains

In this talk, a nonparametric method for density estimation over complicated spatial domains is presented. The method combines a likelihood approach with a regularization based on a differential operator, and the estimator is proven to be consistent. The discretization of the estimator is based on finite elements, ensuring high computational efficiency and enabling great flexibility. The proposed method efficiently deals with data scattered over two-dimensional regions having complicated shapes, two-dimensional Riemannian manifolds, or planar networks. Moreover, it captures very well complicated signals having multiple modes with different directions and intensities of anisotropy.