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

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Resumé

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.

OriginalsprogEngelsk
TidsskriftScandinavian Journal of Statistics
Antal sider23
ISSN0303-6898
DOI
StatusE-pub ahead of print - 2019

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Subsampling
Mixing Processes
Variance Estimator
Point Process
Central limit theorem
Spatial Point Process
Estimator
Covariance matrix
Multivariate Statistics
Statistics
Estimating Function
Ellipsoid
Asymptotic Normality
Asymptotic Properties
Confidence interval
Simulation Study
Point process

Citer dette

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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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AB - 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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