New preprint: Simplified simplicial depth for regression and autoregressive growth processes

A new preprint joint with Christoph P. Kustosz and  Christine H. Müller about “Simplified simplicial depth for regression and autoregressive growth processes” is online as a SFB 823 discussion paper. Abstract: We simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting…

New preprint: Two-sample U-statistic processes for long-range dependent data

A new preprint joint with Aeneas Rooch and Herold Dehling about “Two-sample U-statistic processes for long-range dependent data” is online at arXiv. Abstract: Motivated by some common-change point tests, we investigate the asymptotic distribution of the U-statistic process $U_n(t)=\sum_{i=1}^{[nt]}\sum_{j=[nt]+1}^n h(X_i,X_j)$, 0≤t≤1, when the underlying data are long-range dependent. We present two approaches, one based on an expansion…

New preprint: Convergence of U-statistics indexed by a random walk to stochastic integrals of a Levy sheet

A new preprint joint with Brice Franke and Françoise Pène about “Convergence of U-statistics indexed by a random walk to stochastic integrals of a Levy sheet” is online at arXiv. Abstract: We establish limit theorems for U-statistics indexed by a random walk on Z^d and we express the limit in terms of some Levy sheet…

New Preprint: Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics

A new preprint joint with Herold Dehling and Olimjon Sh. Sharipov about „Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics“ is online at arXiv. Abstract: Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their…

New Preprint: Change-Point Detection under Dependence Based on Two-Sample U-Statistics

A new preprint joint with Herold Dehling, Roland Fried and Isabel García about „Change-Point Detection under Dependence Based on Two-Sample U-Statistics“ is online at arXiv. Abstract: We study the detection of change-points in time series. The classical CUSUM statistic for detection of jumps in the mean is known to be sensitive to outliers. We thus…

New Preprint: Stable Limit Theorem for U-Statistic Processes Indexed by a Random Walk

A new preprint joint with Brice Franke about „Stable Limit Theorem for U-Statistic Processes Indexed by a Random Walk“ is online at arXiv. Abstract: Let (S_n)_{n\in\N} be a random walk in the domain of attraction of an α-stable Lévy process and (\xi(n))_{n\in\N} a sequence of iid random variables (called scenery). We want to investigate U-statistics…