Daniel Vogel

Elliptical graphical modelling

We propose elliptical graphical models based on conditional uncorrelatedness as a robust generalization of Gaussian graphical models. Letting the population distribution be elliptical instead of normal allows the fitting of data with arbitrarily heavy tails. We study the class of proportionally affine equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling. This leads to a new class of partial correlation estimators and analogues of the classical deviance test. General expressions for the asymptotic variance of partial correlation estimators, unconstrained and under decomposable models, are given, and the asymptotic chi square approximation for the pseudo-deviance test statistic is proved. The feasibility of our approach is demonstrated by a simulation study, using, among others, Tylers scatter estimator, which is distribution-free within the elliptical model. Copyright 2011, Oxford University Press.

A fluctuation test for constant Spearman's rho with nuisance-free limit distribution

A CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearmans rho in arbitrary dimensions is proposed. Since the new test does not require the existence of any moments, the applicability on usually heavy-tailed financial data is greatly improved. The asymptotic null distribution is calculated using an invariance principle for the sequential empirical copula process. The limit distribution is free of nuisance parameters and critical values can be obtained without bootstrap techniques. A local power result and an analysis of the behavior of the test in small samples are provided.

The spatial sign covariance matrix with unknown location

The consistency and asymptotic normality of the spatial sign covariance matrix with unknown location are shown. Simulations illustrate the different asymptotic behaviors when using the mean and the spatial median as a location estimator.

Testing for changes in Kendall’s tau

For a bivariate time series

SPATIAL SIGN CORRELATION

((X_i,Y_i))_{i=1,...,n}

Estimation of the variance of partial sums of dependent processes

we want to detect whether the correlation between

On Robust Gaussian Graphical Modeling

X_i

A fluctuation test for constant Spearman’s rho

and

Asymptotics of the two-stage spatial sign correlation

Y_i

Robust estimators for nondecomposable elliptical graphical models

stays constant for all