3,659 research outputs found
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
On the efficiency of Gini's mean difference
18 pages, 3 figures, 8 tables Acknowledgments We are indebted to Herold Dehling for introducing us to the theory of U-statistics, to Roland Fried for introducing us to robust statistics, and to Alexander Dürre, who has demonstrated the benefit of complex analysis for solving statistical problems. Both authors were supported in part by the Collaborative Research Centre 823 Statistical modelling of nonlinear dynamic processes.Peer reviewedPreprin
Studentized U-quantile processes under dependence with applications to change-point analysis
Many popular robust estimators are -quantiles, most notably the
Hodges-Lehmann location estimator and the scale estimator. We prove a
functional central limit theorem for the sequential -quantile process
without any moment assumptions and under weak short-range dependence
conditions. We further devise an estimator for the long-run variance and show
its consistency, from which the convergence of the studentized version of the
sequential -quantile process to a standard Brownian motion follows. This
result can be used to construct CUSUM-type change-point tests based on
-quantiles, which do not rely on bootstrapping procedures. We demonstrate
this approach in detail at the example of the Hodges-Lehmann estimator for
robustly detecting changes in the central location. A simulation study confirms
the very good robustness and efficiency properties of the test. Two real-life
data sets are analyzed
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
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
- …