Brillinger mixing of determinantal point processes and statistical applications

2015/07/23 by Christophe A. N. Biscio, Christophe Ange Napoléon Biscio, Biscio, Christophe Ange Napoléon +2 · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Random Matrices and Applications #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1507.06506

arxiv created 2015/07/23 · openalex publication_date 2015/07/23 · arxiv updated 2015/07/24 · openalex created_date 2022/02/25 · openalex updated_date 2026/07/28

Abstract

Stationary determinantal point processes are proved to be Brillinger mixing. This property is an important step towards asymptotic statistics for these processes. As an important example, a central limit theorem for a wide class of functionals of determinantal point processes is established. This result yields in particular the asymptotic normality of the estimator of the intensity of a stationary determinantal point process and of the kernel estimator of its pair correlation.

Citations

• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
• Determinantal point processes for machine learning

Cited by

• Standard and robust intensity parameter estimation for stationary determinantal point processes
• Box-Covariances of Hyperuniform Point Processes
• On the Variance of the Area of Planar Cylinder Processes Driven by Brillinger-Mixing Point Processes

Related

• Mixing properties and central limit theorem for associated point processes
• Contrast estimation for parametric stationary determinantal point processes
• Stationary determinantal processes: ψ-mixing property and L^q-dimensions
• Asymptotic approximation of the likelihood of stationary determinantal point processes
• Asymptotic properties of maximum likelihood estimators for determinantal point processes