Near-Gaussian entropic functional calculation and density estimation using an asymptotic series
Abstract
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of standard perturbation expansions in quantum field theory. We give novel results on the low-order effects of non-Gaussian even moments and asymmetry (e.g. skewness) on the entropy. The asymptotic expansion is also used to define a best fit maximum entropy density given a set of observed low order moments. The maximum entropy density estimation technique consists simply of the solution of a small set of algebraic equations and is therefore more straightforward numerically than classical maximum-entropy methods which rely on sophisticated convex optimization techniques.
Cite
@article{arxiv.1606.01382,
title = {Near-Gaussian entropic functional calculation and density estimation using an asymptotic series},
author = {Gordon V. Chavez and Richard Kleeman},
journal= {arXiv preprint arXiv:1606.01382},
year = {2016}
}