Prof. Dr. Roland Fried
Was 


Wann 
29.01.2010 von 11:15 bis 13:00 
Wo  Eckerstr. 1, Raum 404 
Name  Kristin Ohneberg 
Kontakttelefon  0761/2037701 
Termin übernehmen 
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Robust partial correlation graphs
Roland Fried
fried@statistik.tudortmund.de
Daniel Vogel
daniel.vogel@tudortmund.de
Technische Universität Dortmund,
44221 Dortmund, Germany
Graphical models allow a simple graphical visualization of the (conditional) dependence structure among multiple variables: each variable is represented by a vertex, and conditional dependence between a pair of variables given all the other variables is illustrated by connecting the corresponding pair of vertices by an edge. Within the Gaussian framework, conditional independence is equivalent to zero partial correlation, i.e. we just need to estimate the partial correlation between each pair of variables and test whether it is zero or not in order to decide on the inclusion of edges in the graph. The arising diagram can thus be called a partial correlation graph.
In this talk we treat two extensions of Gaussian graphical models. Brillinger (1996) and Dahlhaus (2000) suggest to explore the linear dependence structure among multivariate time series by analyzing the partial spectral coherences between the component processes. These are a natural generalization of the partial correlations to the frequency domain. Fried and Didelez (2003) show how to perform stepwise model selection in this context by estimating the partial spectral coherences from suitably chosen subsets of the component processes.
Another generalization of Gaussian graphical models are 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 show how they can be used to derive generalizations of classical Gaussian graphical modelling tools derived from the empirical covariance matrix and the adjusted deviance tests. We demonstrate the feasibility of our approach by a simulation study, using, among others, Tyler's scatter estimator (Tyler, 1987), which is distributionfree within the elliptical model. This technique is in particular suited to robustify the established, likelihoodbased Gaussian graphical modelling methods, which are known to be very sensitive to model misspecifications and outlying observations. Some of the results are summarized in Vogel and Fried (2009).
The robust fitting of partial correlation graphs to multivariate time series data, e.g. by extending the ideas of elliptical graphical modelling to the time series context, is the scope of future research.
References
[1] D. R. Brillinger. Remarks concerning graphical models for time series and point
processes. Revista de Econometria, 16:123, 1996.
[2] R. Dahlhaus. Graphical interaction models for multivariate time series.
Metrika,
51:157172, 2000.
[3] R. Fried and V. Didelez. Decomposability and selection of graphical models for
multivariate time series. Biometrika, 90: 251267, 2003.
[4] D. E. Tyler. A distributionfree Mestimator of multivariate scatter.
Annals of Statistics, 15:234251, 1987.
[5] D. Vogel and R. Fried. On robust Gaussian graphical modelling.
Discussion Paper
36/2009, SFB 823, Technische UniversitÄat Dortmund, 2009.