Spectral Density Ratio Models for Multivariate Extremes
Miguel de Carvalho, Anthony C. Davison
Ecole Polytechnique Fédérale de Lausanne, Switzerland

The joint modelling of extremal events has been a subject of considerable attention both theoretically and in applications. Despite the interest in the comovement of tail events, all approaches known in the literature consider only a spectral distribution function whereas in some applications K independent sources of information are available, each being characterized by a certain covariate x_k. Just as there is a rationale for not modelling multivariate extreme values through univariate techniques, there are also strong reasons for not modelling individually the spectral density corresponding to each of the samples. Particularly, such approach would not only be ineffective in assessing the role that the covariate x_k would play in the interaction of extremes, as it would be a wasteful of data. This paper proposes a semiparametric formulation through which a family of K unknown spectral densities is linked by dint of a weight function and constrained to satisfy a set of marginal moment conditions. Empirical likelihood inference and estimation for this spectral density ratio model is here obtained. An application is given wherein we contrast extreme temperatures under forest-cover versus open-site over 14 different locations in Switzerland.

Keywords: Empirical likelihood; Exponential tilt; Multivariate extreme values; Spectral distribution

Biography: Miguel de Carvalho is a post-doctoral researcher at the Ecole Polytechnique Fédérale de Lausanne under the supervision of Anthony C. Davison; he holds a PhD in Mathematical Statistics obtained at the Universidade Nova de Lisboa – Portugal.