Multivariate Normal Approximation for Functionals of Random Polytopes

Autor(en): Grygierek, Jens
Stichwörter: Central limit theorem; CENTRAL LIMIT-THEOREMS; f-vector; Intrinsic volumes; Mathematics; Multivariate limit theorem; Oracle estimator; POINTS; Poisson point process; PROOF; Random convex hull; Random polytope; Statistics & Probability; Stochastic geometry; VARIANCE ASYMPTOTICS; Volume estimation; VOLUMES
Erscheinungsdatum: 2021
Herausgeber: SPRINGER/PLENUM PUBLISHERS
Journal: JOURNAL OF THEORETICAL PROBABILITY
Volumen: 34
Ausgabe: 2
Startseite: 897
Seitenende: 922
Zusammenfassung: 
Consider the random polytope that is given by the convex hull of a Poisson point process on a smooth convex body in Rd. We prove central limit theorems for continuous motion invariant valuations including the Wills functional and the intrinsic volumes of this random polytope. Additionally we derive a central limit theorem for the oracle estimator that is an unbiased and minimal variance estimator for the volume of a convex set. Finally we obtain a multivariate limit theorem for the intrinsic volumes and the components of the f-vector of the random polytope.
ISSN: 08949840
DOI: 10.1007/s10959-020-00985-3

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