A Non-Classical Parameterization for Density Estimation Using Sample Moments

Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely affects the performance. In this paper, which is a very preliminary version, we propose a non-classical parametrization for density estimation using the sample moments, which does not require the choice of such functions. The parametrization is induced by the squared Hellinger distance, and the solution of it, which is proved to exist and be unique subject to simple prior that does not depend on data, can be obtained by convex optimization. Simulation results show the performance of the proposed estimator in estimating multi-modal densities which are mixtures of different types of functions, with a comparison to the prevailing methods.