Consistency of the Takens estimator for the correlation dimension
Borovkova, S. ; Burton, R. ; Dehling, H.
Ann. Appl. Probab., Tome 9 (1999) no. 1, p. 376-390 / Harvested from Project Euclid
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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.
Publié le : 1999-05-14
Classification:  $U$-statistics,  correlation dimension,  Takens estimator,  ergodic sequences,  absolute regularity,  60F05,  62M10,  62G05,  60G10 
@article{1029962747,
     author = {Borovkova, S. and Burton, R. and Dehling, H.},
     title = {Consistency of the Takens estimator for the correlation
		 dimension},
     journal = {Ann. Appl. Probab.},
     volume = {9},
     number = {1},
     year = {1999},
     pages = { 376-390},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1029962747}
}

Borovkova, S.; Burton, R.; Dehling, H. Consistency of the Takens estimator for the correlation
		 dimension. Ann. Appl. Probab., Tome 9 (1999) no. 1, pp.  376-390. http://gdmltest.u-ga.fr/item/1029962747/