The Annals of Applied Probability

Consistency of the Takens estimator for the correlation dimension

S. Borovkova, R. Burton, and H. Dehling

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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.

Article information

Ann. Appl. Probab. Volume 9, Number 2 (1999), 376-390.

First available in Project Euclid: 21 August 2002

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G05: Estimation 60G10: Stationary processes

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


Borovkova, S.; Burton, R.; Dehling, H. Consistency of the Takens estimator for the correlation dimension. Ann. Appl. Probab. 9 (1999), no. 2, 376--390. doi:10.1214/aoap/1029962747.

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