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The modeling of dependence between maxima is an important subject in several applications in risk analysis. To this aim, the extreme value copula function, characterized via the madogram, can be used as a margin-free description of the dependence structure. From a practical point of view, the family of extreme value distributions is very rich and arise naturally as the limiting distribution of properly normalized component-wise maxima. In this paper, we investigate the nonparametric estimation of the madogram where data are completely missing at random. We provide the functional central limit theorem for the considered multivariate madrogram correctly normalized, towards a tight Gaussian process for which the covariance function depends on the probabilities of missing. Explicit formula for the asymptotic variance is also given. Our results are illustrated in a finite sample setting with a simulation study. Our method is also illustrated on a sparse dataset of annual maxima rainfall in Central Eastern Canada. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the problem of estimating the tail of a bivariate distribution function. To this end we develop a general extension of the POT (peaks-over-threshold) method, mainly based on a two-dimensional version of the Pickands–Balkema–de Haan Theorem. We introduce a new parameter that describes the nature of the tail dependence, and we provide a way to estimate it. We construct a two-dimensional tail estimator and study its asymptotic properties. We also present real data examples which illustrate our theoretical results. [Copyright &y& Elsevier]

This paper deals with the problem of estimating the level sets L(c) = {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) = {Fn(x) ≥ c}. In our setting, non-compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by applications in multivariate risk theory. In particular we propose a new bivariate version of the conditional tail expectation by conditioning the two-dimensional random vector to be in the level set L(c). We also present simulated and real examples which illustrate our theoretical results. [ABSTRACT FROM AUTHOR]