Elliptical graphical modelling in higher dimensions

Daniel Vogel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Simpson’s famous paradox vividly exemplifies the importance of considering conditional, rather than marginal, associations for assessing the dependence structure of several variables. The study of conditional dependencies is the subject matter of graphical models. The statistical methods applied in graphical models for continuous variables rely on the assumption of normality, which leads to the term Gaussian graphical models. We consider elliptical graphical models, that is, we allow the population distribution to be elliptical instead of normal. We examine the class of affine equivariant scatter estimators and propose an adjusted version of the deviance tests, valid under ellipticity. A detailed derivation can be found in [1]. In this exposition we report the results of a simulation study, demonstrating the feasibility of our approach also in higher dimensions. Graphical models based on classical, non-robust estimators have been used, e.g., to explore successfully the partial correlation structure within high-dimensional physiological time series [2] and within high-dimensional time series describing neural oscillators [3].
Original languageEnglish
Title of host publicationProceedings of Biosignal 2010, July 14-16, 2010, Berlin, Germany
Number of pages4
Publication statusPublished - Jul 2010
EventInternational Biosignal Processing Conference (Biosignal) 2010 - Berlin, Germany
Duration: 14 Jul 201016 Jul 2010

Conference

ConferenceInternational Biosignal Processing Conference (Biosignal) 2010
CountryGermany
CityBerlin
Period14/07/1016/07/10

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