期刊
BERNOULLI
卷 25, 期 3, 页码 1724-1754出版社
INT STATISTICAL INST
DOI: 10.3150/18-BEJ1033
关键词
determinantal point process; negative association; parametric estimation; positive association; strong mixing
Positively (resp. negatively) associated point processes are a class of point processes that induce attraction (resp. inhibition) between the points. As an important example, determinantal point processes (DPPs) are negatively associated. We prove alpha-mixing properties for associated spatial point processes by controlling their alpha-coefficients in terms of the first two intensity functions. A central limit theorem for functionals of associated point processes is deduced, using both the association and the alpha-mixing properties. We discuss in detail the case of DPPs, for which we obtain the limiting distribution of sums, over subsets of close enough points of the process, of any bounded function of the DPP. As an application, we get the asymptotic properties of the parametric two-step estimator of some inhomogeneous DPPs.
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