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Normal and non-normal approximation of degenerate U-statistics

Christian Doebler (University of Luxembourg)
Thiele Seminar
Thursday, 15 September, 2016, at 13:15-14:00, in Koll. D (1531-211)

We provide bounds on the Wasserstein distance between the distribution of a degenerate, not necessarily symmetric U-statistic of independent random variables and the standard normal distribution. One main consequence of these bounds is a complete quantitative counterpart to a theorem by P. de Jong from 1990 which states that, under a certain negligibility condition, a sequence of such U-statistics satisfies a CLT whenever the sequence of fourth moments converges to 3.

We will also discuss approximation by a centered Gamma distribution and a generalization of de Jong's theorem to the multivariate case of vectors of such U-statistics.

Finally, if time allows, then we will also address the classical case of symmetric U-statistics.

Organised by: The T.N. Thiele Centre
Contact person: Mark Podolskij