New Preprint: Change-Point Detection and Bootstrap for Hilbert Space Valued Random Fields

A new preprint joint with Béatrice Bucchia about “change-point detection and bootstrap for Hilbert space valued random fields” is online at arXiv.

Abstract: The problem of testing for the presence of epidemic changes in random fields is investigated. In order to be able to deal with general changes in the marginal distribution, a Cramér-von-Mises-type test is introduced which is based on Hilbert space theory. A functional central limit theorem for ρ-mixing Hilbert space valued random fields is proven. In order to avoid the estimation of the long-run variance and obtain critical values, Shao’s dependent wild bootstrap method is adapted to this context. For this, a joint functional central limit theorem for the original and the bootstrap sample is shown. Finally, the theoretic results are supplemented by a short simulation study.

Letter to editor: Common influencing factors are no evidence of association

A comment on an article by Callander, Newman, and Holt (2015) appeared in the Archives of Sexual Behavior pointing out a statistical fallacy: A common set of influencing factors can exist for two (or more) variables, while the random variables are uncorrelated or even independent. This is possible because after controlling for explanatory variables, the…

New preprint: Subsampling for General Statistics under Long Range Dependence

A new preprint joint with Annika Betken about “Subsampling for General Statistics under Long Range Dependence” is online on arXiv. Abstract: Subsampling for General Statistics under Long Range DependenceIn the statistical inference for long range dependent time series, the shape of the limit distribution typically dependents on unknown parameters. Therefore, we propose to use subsampling.…

New preprint: A Robust Method for Shift Detection in Time Series

A new preprint joint with Herold Dehling and Roland Fried about “A Robust Method for Shift Detection in Time Series” is online at arXiv. Abstract: We present a robust test for change-points in time series which is based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on…

New preprint: Bootstrap for U-Statistics: A new approach

A new preprint joint with Olimjon Sh. Sharipov and Johannes Tewes about “Bootstrap for U-Statistics: A new approach” is online at arXiv. Abstract: Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the…

New preprint: Studentized sequential U-quantiles under dependence with applications to change-point analysis

A new preprint joint with Daniel Vogel about “Studentized sequential U-quantiles under dependence with applications to change-point Analysis” is online at arXiv. Abstract: Many popular robust estimators are U-quantiles, most notably the Hodges-Lehmann location estimator and the Q_n scale estimator. We prove a functional central limit theorem for the sequential U-quantile process without any moment…

New preprint: Sequential block bootstrap in a Hilbert space with application to change point analysis

A new preprint joint with Olimjon Sh. Sharipov and Johannes Tewes about “Sequential block bootstrap in a Hilbert space with application to change point analysis” is online at arXiv. Abstract: A new test for structural changes in functional data is investigated. It is based on Hilbert space theory and critical values are deduced from bootstrap…

New preprint: Multivariate generalized linear-statistics of short range dependent data

A new preprint joint with Svenja Fischer and Roland Fried about “Multivariate generalized linear-statistics of short range dependent data” is online at arXiv. Abstract: Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics…

New preprint: The sequential empirical process of a random walk in random scenery

A new preprint about “The sequential empirical process of a random walk in random scenery” is online at arXiv. Abstract: A random walk in random scenery $(Y_n)_{n\in\N}$ is given by $Y_n=\xi_{S_n}$ for a random walk $(S_n)_{n\in\N}$ and iid random variables $(\xi(n))_{n\in\N}$. In this paper, we will show the weak convergence of the sequential empirical process,…

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…