Moment Ideals of Local Dirac Mixtures

Autor(en): Koutsoumpelias, Alexandros Grosdos
Wageringel, Markus
Stichwörter: algebraic statistics; Dirac measure; GEOMETRY; local mixture; Mathematics; Mathematics, Applied; MODELS; moment ideal; Pareto distribution; Prony's method; TANGENTIAL VARIETIES
Erscheinungsdatum: 2020
Herausgeber: SIAM PUBLICATIONS
Journal: SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY
Volumen: 4
Ausgabe: 1
Startseite: 1
Seitenende: 27
Zusammenfassung: 
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.
ISSN: 24706566
DOI: 10.1137/18M1219783

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