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May 1999 Consistency of the Takens estimator for the correlation dimension
S. Borovkova, R. Burton, H. Dehling
Ann. Appl. Probab. 9(2): 376-390 (May 1999). DOI: 10.1214/aoap/1029962747

Abstract

Motivated by the problem of estimating the fractal dimension of a strange attractor, we prove weak consistency of U-statistics for stationary ergodic and mixing sequences when the kernel function is unbounded, extending by this earlier results of Aaronson, Burton, Dehling, Gilat, Hill and Weiss. We apply the obtained results to show consistency of the Takens estimator for the correlation dimension.

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S. Borovkova. R. Burton. H. Dehling. "Consistency of the Takens estimator for the correlation dimension." Ann. Appl. Probab. 9 (2) 376 - 390, May 1999. https://doi.org/10.1214/aoap/1029962747

Information

Published: May 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0928.62072
MathSciNet: MR1687339
Digital Object Identifier: 10.1214/aoap/1029962747

Subjects:
Primary: 60F05 , 62M10
Secondary: 60G10 , 62G05

Keywords: $U$-statistics , absolute regularity , correlation dimension , ergodic sequences , Takens estimator

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.9 • No. 2 • May 1999
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