The tutorials will take place on Friday the 11th of December 2015 and the introductory CRoNoS Winter Course on Robust methods and multivariate extremes will take place the 9-10 December 2015. The registration for the tutorials will take place in the same building. The number of participants to the tutorials is limited and restricted only to those who attend the conference. For further information send an email to info@CMStatistics.org.
Multivariate extreme value theory (MEVT) is the proper toolbox for analyzing several extremal events simultaneously. Its practical relevance in particular for risk assessment is, consequently, obvious. But on the other hand MEVT is by no means easy to access; its key results are formulated in a measure theoretic setup, a fils rouge is not visible.
Writing the 'angular measure' in MEVT in terms of a random vector, however, provides the missing fils rouge: Every result in MEVT, every relevant probability distribution, be it a max-stable one or a generalized Pareto distribution, every relevant copula, every tail dependence coefficient etc. can be formulated using a particular kind of norm on multivariate Euclidean space, called D-norm.
Norms are introduced in each course on mathematics as soon as the multivariate Euclidean space is introduced. The definition of an arbitrary D-norm requires only the additional knowledge on random variables and their expectations. But D-norms do not only constitute the fils rouge through MEVT, they are of particular mathematical interest of their own.
During the optional course we provide in the introductory chapter the theory of D-norms in detail. The second chapter introduces multivariate generalized Pareto distributions and max-stable distributions via D-norms. The third chapter provides the extension of D-norms to functional spaces and, thus, deals with generalized Pareto processes and max-stable processes.
In this tutorial, univariate EVT and D-norms will be reviewed, and a relaxed tour through the essentials of MEVT, due to the D-norms approach, will be provided.Material: Booklet Slides
Nonlinear time series models play an important role in a number of econometric problems; they are pervasive in financial econometrics. Examples include AR-ARCH models, discretely observed non-Gaussian Ornstein-Uhlenbeck processes, autoregressive conditional duration models for irregularly sampled data, ... Although Gaussian assumptions, in that context, are quite unrealistic, Gaussian quasi-likelihood procedures (for estimation and testing) remain the most popular approach. Those methods, typically, are not validity-robust---namely, their validity (asymptotic probability level for tests, root-n consistency for estimators) is not guaranteed.
In principle, traditional semiparametric inference methods (in the style of Bickel et al. 1993) offer a theoretical alternative. However, they require tedious tangent space calculations, and the estimation of the actual innovation density. The objective of this tutorial is to show that rank-based inference constitutes a convenient substitute for those methods, and yield validity-robust tests and estimators reaching semiparametric efficiency bounds without running into the difficulties of tangent space calculation and density estimation.
Material: Paper1 Paper2 Paper3
Slides: Tutorial LeCam in a Nutshell Semiparametrics Regression Stable