3,608 research outputs found

    On generalizing Gaussian graphical models

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    Asymptotics of the two-stage spatial sign correlation

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    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

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    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

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    Many popular robust estimators are UU-quantiles, most notably the Hodges-Lehmann location estimator and the QnQ_n scale estimator. We prove a functional central limit theorem for the sequential UU-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 UU-quantile process to a standard Brownian motion follows. This result can be used to construct CUSUM-type change-point tests based on UU-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

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    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

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    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
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