Moment ideals of local Dirac mixtures
Commutative Algebra
2020-02-03 v2 Statistics Theory
Statistics Theory
Abstract
In this paper we study ideals arising from moments of local Dirac measures and their mixtures. We provide generators for the case of first order local Diracs and explain how to obtain the moment ideal of the Pareto distribution from them. We then use elimination theory and Prony's method for parameter estimation of finite mixtures. Our results are showcased with applications in signal processing and statistics. We highlight the natural connections to algebraic statistics, combinatorics and applications in analysis throughout the paper.
Keywords
Cite
@article{arxiv.1809.09934,
title = {Moment ideals of local Dirac mixtures},
author = {Alexandros Grosdos Koutsoumpelias and Markus Wageringel},
journal= {arXiv preprint arXiv:1809.09934},
year = {2020}
}
Comments
26 pages, 3 figures