Consistency of the Takens estimator for the correlation dimension
type: Item
instance of: scholarly article
title: Consistency of the Takens estimator for the correlation dimension
zbMATH Open document ID: 0928.62072
published in: The Annals of Applied Probability
publication date: 2000-01-11T00:00:00Z
review text: \textit{J. Aaronson} et al. [Trans. Am. Math. Soc. 348, No. 7, 2845-2866 (1996; Zbl 0863.60032)] proved consistency results for U-statistics of stationary ergodic, respectively absolutely regular, sequences under the condition that the kernel \(h(x,y)\) is bounded. In this paper, replacing their condition on \( (x,y)\) by a uniform integrability requirement on \(h(X_i,Y_j)\), \(i,j\geq 1\), the authors extend their results. The results obtained enable us to show consistency of the Takens estimator for the correlation dimension, which is a good measure of the complexity of the dynamics.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 1346301
zbMATH Keywords: ergodic sequences
zbMATH Keywords: absolute regularity
zbMATH Keywords: U-statistics
zbMATH Keywords: Takens estimator
zbMATH Keywords: correlation dimension
author: Svetlana Borovkova
author: Robert Burton
author: Herold Dehling
reviewed by: Ken-ichi Yoshihara
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1029962747
OpenAlex ID: W2069377542
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DOI: 10.1214/AOAP/1029962747
description: scientific article; zbMATH DE number 1346301