This quarterly seminar series features presentations from leading researchers in Extreme Value Analysis, both from within the Netherlands and internationally. The next seminar will be held at  on October 16, 2024. You might also check our website: https://evta-seminar.nl.

• 13:30-14:15 Frank Röttger (Eindhoven University of Technology)

Location: Room K1203

Title: Directed graphical models and structural causal models in multivariate extremes from threshold exceedances

Abstract: The recent introduction of conditional independence in multivariate extremes from threshold exceedances opened many new research directions in extremal dependence modeling. In particular, many papers have considered undirected graphical models based on this new notion of extremal conditional independence. In this talk we introduce directed graphical models based on extremal conditional independence, and discuss the resulting directed extremal Markov properties as well as Markov equivalence. Furthermore, we introduce a limiting extremal SCM that conforms with our directed extremal Markov properties. For the parametric subclass of Hüsler–Reiss distributions, we find a simple linear extremal SCM that permits a parametric description of extremal conditional independence. This gives rise to an extremal conditional independence test, which we implement in a PC-type algorithm. Finally, we demonstrate our approach on real data.

This is joint work with Sebastian Engelke and Nicola Gnecco.

• 14:15-14:45 Coffee break

• 14:45-15:45 Abdelaati Daouia (Toulouse School of Economics)

Location: Room K1206

Title: Extremal regression in heavy-tailed models

Abstract: Studying rare events at the heavy tails of Pareto-type distributions, in the presence of high-dimensional covariates, is a burgeoning science and has many applications both in and out of finance. Most attempts to tackle the subject involve quantile regression, which usually offers a natural way of examining the impact of covariates at different levels of the dependent variable. In risk management, however, quantiles are often criticized for their failure to be subadditive in general, and for their lack of sensitivity to the magnitude of extreme losses. This bolstered the interest in their least squares analogs, coined as expectiles, which define the only coherent law-invariant risk measure that is also elicitable, namely, they benefit from a straightforward backtesting methodology. For the estimation of both extreme conditional quantiles and expectiles, we develop a general theory using a flexible tail location-scale quantile regression model with heavy-tailed noise. We introduce versatile residual-based estimators of extremal regression quantiles and expectiles and derive their asymptotic properties in a general setting. We then tailor the discussion to the linear and local linear estimation settings. We showcase the performance of our procedures in a detailed simulation study and apply them to concrete financial data.

Location:

Location: Room 1203 & 1206 (see above for details), Koopmans Building, Tilburg School of Economics and Management
Address: Warandelaan 2, 5037AB Tilburg