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A general central limit theorem and a subsampling variance estimator for α ‐mixing point processes
Author(s) -
Biscio Christophe Ange Napoléon,
Waagepetersen Rasmus
Publication year - 2019
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.12389
Subject(s) - mathematics , central limit theorem , estimator , delta method , mixing (physics) , statistics , covariance , limit (mathematics) , asymptotic distribution , covariance matrix , point process , mathematical analysis , physics , quantum mechanics
We establish a central limit theorem for multivariate summary statistics of nonstationary α ‐mixing spatial point processes and a subsampling estimator of the covariance matrix of such statistics. The central limit theorem is crucial for establishing asymptotic properties of estimators in statistics for spatial point processes. The covariance matrix subsampling estimator is flexible and model free. It is needed, for example, to construct confidence intervals and ellipsoids based on asymptotic normality of estimators. We also provide a simulation study investigating an application of our results to estimating functions.