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A general central limit theorem and a subsampling variance estimator for α‐mixing point processes

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  • Christophe Ange Napoléon Biscio
  • Rasmus Waagepetersen

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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  • Christophe Ange Napoléon Biscio & Rasmus Waagepetersen, 2019. "A general central limit theorem and a subsampling variance estimator for α‐mixing point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(4), pages 1168-1190, December.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:4:p:1168-1190
    DOI: 10.1111/sjos.12389
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    Cited by:

    1. Mohammad Ghorbani & Ottmar Cronie & Jorge Mateu & Jun Yu, 2021. "Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 529-568, September.
    2. Miryam S. Merk & Philipp Otto, 2022. "Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross‐sectional resampling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.

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