Consistency of the Takens estimator for the correlation dimension

S. Borovkova*, Robert Burton, H. Dehling

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)376-390
Number of pages15
JournalAnnals of Applied Probability
Volume9
Issue number2
DOIs
Publication statusPublished - May 1999

Keywords

  • Absolute regularity
  • Correlation dimension
  • Ergodic sequences
  • Takens estimator
  • U-statistics

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