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Moment ideals of local Dirac mixtures. (English) Zbl 1436.13059

The authors consider ideals arising from moments of local Dirac measures and their mixtures. More precisely, generators for the case of first order local Diracs are obtained and it is explained how to obtain the moment ideal of the Pareto distribution from them. Afterwards, it is shown how elimination theory and Prony’s method can be applied for parameter estimation of finite mixtures. Throughout the paper, the authors highlight the connections to algebraic statistics, combinatorics, as well as applications in analysis and in signal processing.

MSC:

13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
62F10 Point estimation
14Q10 Computational aspects of algebraic surfaces
65T40 Numerical methods for trigonometric approximation and interpolation
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