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Contrast estimation for parametric stationary determinantal point processes. (English) Zbl 1361.60034
Summary: 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).

##### MSC:
 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 60F05 Central limit and other weak theorems 62F10 Point estimation 62F12 Asymptotic properties of parametric estimators 62E20 Asymptotic distribution theory in statistics
R; spatstat
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