Consistency of the Takens estimator for the correlation dimension
\textit{J. Aaronson} et al. [Trans. Am. Math. Soc. 348, No. 7, 2845-2866 (1996; Zbl 0863.60032)] proved consistency results for U-statistics of stationary ergodic, respectively absolutely regular, sequences under the condition that the kernel \(h(x,y)\) is bounded. In this paper, replacing their condition on \( (x,y)\) by a uniform integrability requirement on \(h(X_i,Y_j)\), \(i,j\geq 1\), the authors extend their results. The results obtained enable us to show consistency of the Takens estimator for the correlation dimension, which is a good measure of the complexity of the dynamics.
scientific article; zbMATH DE number 1346301