Premium
Contrast Estimation for Parametric Stationary Determinantal Point Processes
Author(s) -
Biscio Christophe Ange Napoléon,
Lavancier Frédéric
Publication year - 2017
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12249
Subject(s) - mathematics , point process , determinantal point process , complement (music) , stationary point , asymptotic distribution , mixing (physics) , parametric statistics , contrast (vision) , consistency (knowledge bases) , property (philosophy) , mathematical proof , pure mathematics , statistical physics , mathematical analysis , discrete mathematics , statistics , random matrix , geometry , artificial intelligence , estimator , philosophy , chemistry , computer science , biochemistry , eigenvalues and eigenvectors , physics , complementation , gene , phenotype , epistemology , quantum mechanics
We study minimum contrast estimation for parametric stationary determinantal point processes. These processes form a useful class of models for repulsive (or regular, or inhibitive) point patterns and are already applied in numerous statistical applications. Our main focus is on minimum contrast methods based on the Ripley's K ‐function or on the pair correlation function. Strong consistency and asymptotic normality of theses procedures are proved under general conditions that only concern the existence of the process and its regularity with respect to the parameters. A key ingredient of the proofs is the recently established Brillinger mixing property of stationary determinantal point processes. This work may be viewed as a complement to the study of Y. Guan and M. Sherman who establish the same kind of asymptotic properties for a large class of Cox processes, which in turn are models for clustering (or aggregation).