Consistency of the Takens estimator for the correlation dimension

Authors
Borovkova, S Burton, R Dehling, H
Citation
S. Borovkova et al., Consistency of the Takens estimator for the correlation dimension, ANN APPL PR, 9(2), 1999, pp. 376-390
Citations number
11
Categorie Soggetti
Mathematics
Journal title
ANNALS OF APPLIED PROBABILITY
ISSN journal
10505164 → ACNP
Volume
9
Issue
2
Year of publication
1999
Pages
376 - 390
Database
ISI
SICI code
1050-5164(199905)9:2<376:COTTEF>2.0.ZU;2-3
Abstract
Motivated by the problem of estimating the fractal dimension of a strange a ttractor, we prove weak consistency of U-statistics for stationary ergodic and mixing sequences when the kernel function is unbounded, extending by th is earlier results of Aaronson, Burton, Dehling, Gilat, Hill and Weiss. We apply the obtained results to show consistency of the Takens estimator for the con-elation dimension.