A geometric approach to density estimation with additive noise.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 L 2 -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.
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