Abstract: We introduce and study a method for density estimation under an additive noise model. Our method does not attempt to maximize a likelihood, but rather is purely geometric: heuristically, we -project the observed empirical distribution onto the space of candidate densities that are reachable under the additive noise model. Our estimator reduces to a quadratic program, and so can be computed efficiently. In simulation studies, it roughly matches the accuracy of fully general maximum likelihood estimators at a fraction of the computational cost. We give a theoretical analysis of the estimator and show that it is consistent, attains a quasi-parametric convergence rate under moment conditions, and is robust to model mis-specification. We provide an R implementation of the proposed estimator in the package nlpden.

Key words and phrases: M-estimator, minimum distance estimator, mixture model, quadratic program, shape constrained estimator.