Brillinger mixing of determinantal point processes and statistical\n applications

2015/07/23 by Christophe A. N. Biscio, Biscio, Christophe Ange Napoléon, Frédéric Lavancier +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1507.06506

openalex publication_date 2015/07/23 · openalex created_date 2022/02/25 · openalex updated_date 2026/07/28

Abstract

Stationary determinantal point processes are proved to be Brillinger mixing.\nThis property is an important step towards asymptotic statistics for these\nprocesses. As an important example, a central limit theorem for a wide class of\nfunctionals of determinantal point processes is established. This result yields\nin particular the asymptotic normality of the estimator of the intensity of a\nstationary determinantal point process and of the kernel estimator of its pair\ncorrelation.\n

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

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