A general central limit theorem and a subsampling variance estimator for α‐mixing point processes |
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Authors: | Christophe Ange Napol on Biscio,Rasmus Waagepetersen |
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Affiliation: | Christophe Ange Napoléon Biscio,Rasmus Waagepetersen |
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Abstract: | 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. |
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Keywords: | α ‐mixing central limit theorem estimating function marked point process spatial point process subsampling |
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