2 research outputs found
Moment ideals of local Dirac mixtures
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.Comment: 26 pages, 3 figure
Algebraic Methods for the Estimation of Statistical Distributions
This thesis deals with the problem of estimating statistical distributions from data. In the first part, the method of moments is used in combination with computational algebraic techniques in order to estimate parameters coming from local Dirac mixtures and their convolutions. The second part focuses on the nonparametric setting, in particular on combinatorial and algebraic aspects of the estimation of log-concave distributions