arXiv subjects

Herold G. Dehling

Publications and source records attributed to Herold G. Dehling.

3 recordsLinked to original sources

arXiv2023

U-statistics of local sample moments under weak dependence

In this paper, we study the asymptotic distribution of some U-statistics whose entries are functions of empirical moments computed from non-overlapping consecutive blocks of an underlying weakly dependent process. The length of these blocks converges to infinity, and thus we consider U-statistics of triangular arrays. We establish asymptotic normality of such U-statistics. The results can be used to construct tests for changes of higher order moments.

math.PR↗

arXiv2023

Some remarks on the ergodic theorem for $U$-statistics

In this note, we investigate the convergence of a $U$-statistic of order two having stationary ergodic data. We will find sufficient conditions for the almost sure and $L^1$ convergence and present some counter-examples showing that the $U$-statistic itself might fail to converge: centering is needed as well as boundedness of $\sup_{j\geq 2}\mathbb{E}[|h(X_1,X_j)|]$.

math.PR↗

arXiv2013

Weak convergence of the empirical process of intermittent maps in L2 under long-range dependence

We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical distribution function, suitably normalized, converges to a degenerate stable process, and we give the corresponding almost sure result. We apply the results to the convergence of the Wasserstein distance between the empirical measure and the invariant measure. We also apply it to obtain the asymptotic distribution of the corresponding Cramér-von-Mises statistic.

math.PR↗