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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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.

Article information

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

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1029962747

Mathematical Reviews number (MathSciNet)
MR1687339

Digital Object Identifier
doi:10.1214/aoap/1029962747

Zentralblatt MATH identifier
0928.62072

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

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

Citation

Borovkova, S.; Burton, R.; Dehling, H. Consistency of the Takens estimator for the correlation dimension. The Annals of Applied Probability 9 (1999), no. 2, 376--390. doi:10.1214/aoap/1029962747. http://projecteuclid.org/euclid.aoap/1029962747.


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References

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