Multiscale local polynomial density estimation

Abstract. The multiscale local polynomial transform (MLPT) is a combination of a kernel method for non parametric regression or density estimation with a projection onto a basis in a multiscale framework. The MLPT is proposed for the estimation of densities with possibly one or more singular points at unknown locations. The proposed estimator reformulates the density estimation problem as a high-dimensional, sparse regression problem with asymptotically exponential response variables. The covariates in this model are the observations from the unknown density themselves. The design matrix comes from a novel extension of the MLPT for use on highly non equidistant data.