Green's function based unparameterised multi-dimensional kernel density and likelihood ratio estimator

Abstract

This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary likelihood estimator for classification purposes, so issues such as mis-modeling and overtraining are also discussed. The identity behind the density estimator can be interpreted as a real-valued, non-scalar kernel method which is able to reconstruct differentiable density functions.