# 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.

Originalsprog Engelsk Scandinavian Journal of Statistics 23 0303-6898 https://doi.org/10.1111/sjos.12389 E-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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title = "A general central limit theorem and a subsampling variance estimator for α‐mixing point processes",
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.",
author = "Christophe Biscio and Rasmus Waagepetersen",
year = "2019",
doi = "10.1111/sjos.12389",
language = "English",
journal = "Scandinavian Journal of Statistics",
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publisher = "Wiley-Blackwell",

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I: Scandinavian Journal of Statistics, 2019.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - A general central limit theorem and a subsampling variance estimator for α‐mixing point processes

AU - Biscio, Christophe

AU - Waagepetersen, Rasmus

PY - 2019

Y1 - 2019

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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.

U2 - 10.1111/sjos.12389

DO - 10.1111/sjos.12389

M3 - Journal article

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

ER -