Asymptotics of the two-stage spatial sign correlation

Acknowledgments This research was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. The authors wish to thank the editors and referees for their careful handling of the manuscript. They further acknowledge the anonymous referees of the article Spatial sign correlation (J. Multivariate Anal. 135, pages 89–105, 2015), who independently of each other suggested to further explore the properties of two-stage spatial sign correlation.Non peer reviewedPreprin

Spatial Sign Correlation

A new robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied and compared to other robust correlation estimators by means of numerical simulations.Comment: 20 pages, 7 figures, 2 table

The spatial sign covariance matrix and its application for robust correlation estimation

8 pages, 2 figures, to be published in the conference proceedings of 11th international conference "Computer Data Analysis & Modeling 2016" http://www.ajs.or.at/index.php/ajs/about/editorialPolicies#openAccessPolicyPeer reviewedPublisher PD

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Acknowledgments Alexander Dürre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.Non peer reviewedPostprin

Robust change-point detection and dependence modeling

This doctoral thesis consists of three parts: robust estimation of the autocorrelation function, the spatial sign correlation, and robust change-point detection in panel data. Albeit covering quite different statistical branches like time series analysis, multivariate analysis, and change-point detection, there is a common issue in all of the sections and this is robustness. Robustness is in the sense that the statistical analysis should stay reliable if there is a small fraction of observations which do not follow the chosen model. The first part of the thesis is a review study comparing different proposals for robust estimation of the autocorrelation function. Over the years many estimators have been proposed but thorough comparisons are missing, resulting in a lack of knowledge which estimator is preferable in which situation. We treat this problem, though we mainly concentrate on a special but nonetheless very popular case where the bulk of observations is generated from a linear Gaussian process. The second chapter deals with something congeneric, namely measuring dependence through the spatial sign correlation, a robust and within the elliptic model distribution-free estimator for the correlation based on the spatial sign covariance matrix. We derive its asymptotic distribution and robustness properties like influence function and gross error sensitivity. Furthermore we propose a two stage version which improves both efficiency under normality and robustness. The surprisingly simple formula of its asymptotic variance is used to construct a variance stabilizing transformation, which enables us to calculate very accurate confidence intervals, which are distribution-free within the elliptic model. We also propose a positive semi-definite multivariate spatial sign correlation, which is more efficient but less robust than its bivariate counterpart. The third chapter deals with a robust test for a location change in panel data under serial dependence. Robustness is achieved by using robust scores, which are calculated by applying psi-functions. The main focus here is to derive asymptotics under the null hypothesis of a stationary panel, if both the number of individuals and time points tend to infinity. We can show under some regularity assumptions that the limiting distribution does not depend on the underlying distribution of the panel as long as we have short range dependence in the time dimension and ndependence in the cross sectional dimension

Self-organized critical phenomena

The concept of self-organized criticality was proposed as an explanation for the occurrence of fractal structures in diverse natural phenomena. Roughly speaking the idea behind self-organized criticality is that a dynamic drives a system towards a stationary state that is characterized by power law correlations in space and time. We study two of the most famous models that were introduced as models exhibiting self-organized criticality. The first of them is the forest fire model. In a forest fire model each site (vertex) of a graph is either vacant or occupied by a tree. Vacant sites get occupied according to independent rate 1 Poisson processes. Independently, at each sites ignition (by lightning) occurs according to independent Poisson processes that have rate Lambda>0. When a site is ignited its whole cluster of occupied sites becomes vacant instantaneously. It is known that infinite volume forest fire processes exist for all ignition rates Lambda>0. The proof of existence is rather abstract, and does not imply uniqueness. Nor does the construction answer the question whether infinite volume forest fire processes are measurable with respect to their driving Poisson processes. Motivated by these questions, we show the almost sure infinite volume convergence for forest fire models with respect to their driving Poisson processes. Our proof is quite general and covers all graphs with bounded vertex, all positive ignition rates Lambda>0, and a quite large set of initial configurations. One of the main ingredients of the proof is an estimate for the decay of the cluster size distribution in a forest fire model. For Gamma>0, we study the probability that the cluster at site x and time t>=Gamma is larger than m, conditioned on the configuration of some further clusters at time t. We show that as m tends to infinity, this conditional probability decays to zero. The convergence is uniform in the choice of the site x, the time t, and the configuration of the further clusters we condition on. Being a consequence of almost sure infinite volume convergence, we obtain uniqueness and measurability with respect to the driving Poisson processes, and the Markov property. The second model in focus is the Abelian sandpile model. Let Lambda be a finite subset of the two-dimensional integer lattice. We consider the following sandpile model on Lambda: each vertex in Lambda contains a sandpile with a height between one and four sand grains. At discrete times, we choose a site v in Lambda randomly and add a sand grain at the site v. If after adding the sand grain the height at the site v is strictly larger than four, then the site topples. That is, four sand grains leave the site v, and each distance-one-neighbour of v gets one of these grains. If after toppling the site v there are other sites with a height strictly larger than four, we continue by toppling these sites until we obtain a configuration where all sites have a height between one and four. We study the scaling limit for the height one field in such a sandpile model. More precisely, we identify the scaling limit for the covariance of having height one at two macroscopically distant sites. We show that this scaling limit is conformally covariant. Furthermore, we show a central limit theorem for the sandpile height one field. Our results are based on a representation of the height one joint intensities that is close to a block-determinantal structure

Escritos afroariqueños. Intervenciones políticas frente al multiculturalismo chileno

El presente artículo analiza las dos principales publicaciones de autoría afroariqueña —Lumbanga. Memorias orales de la cultura afrochilena, de Cristián Báez (2010), y Afrochilenos. Una historia oculta, de Marta Salgado (2013)— en cuanto intervenciones políticas destinadas a expresar los posicionamientos de sus autores y autoras en el campo intelectual chileno y, en particular, frente a las políticas del multiculturalismo nacional, a las formas de reconocimiento que en este contexto se hacen posibles y a los racismos que en él se reproducen. Para ello se contextualiza la aparición de autoras y autores afrodescendientes en el campo intelectual latinoamericano, la importancia de generar nuevas narrativas históricas “desde adentro” en el marco del movimiento afrodescendiente latinoamericano, así como las políticas multiculturalistas implementadas a nivel nacional desde la década de 1990. Finalmente, se analizan los textos en cuestión, concluyendo con una reflexión sobre la forma en que estos textos se sitúan en el campo político e intelectual chileno

Die zwei Kentaurengruppen von Antonio Corradini (1688-1752) im Dresdner Großen Garten

1716 schuf der venetianische Bildhauer Antonio Corradini zwei Kentaurengruppen aus Marmor. Um 1730 wurden sie an der Westseite des Palais im Großen Garten aufgestellt und stehen dort bis heute. Es sind Nessus und Deianira und Eurytus und Hippodameia. Die kunstwissenschaftliche Analyse untersucht den Ankauf für Dresden und die Benennung der dargestellten Kentauren und der von ihnen geraubten Frauen