  Probability density estimation is a core problem of statistics and signal
processing. 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, we propose a
non-classical parametrization for density estimation using 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 a simple prior that does not depend on
data, and can be obtained by convex optimization. Statistical properties of the
density estimator, together with an asymptotic error upper bound are proposed
for the estimator by power moments. Applications of the proposed density
estimator in signal processing tasks are given. Simulation results validate the
performance of the estimator by a comparison to several prevailing methods. To
the best of our knowledge, the proposed estimator is the first one in the
literature for which the power moments up to an arbitrary even order exactly
match the sample moments, while the true density is not assumed to fall within
specific function classes.
