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.
"Consistency of the Takens estimator for the correlation dimension." Ann. Appl. Probab. 9 (2) 376 - 390, May 1999. https://doi.org/10.1214/aoap/1029962747