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Title: Extremal dependence between maxima of concomitants Authors:  Amir Khorrami Chokami - University of Turin (Italy) [presenting]
Marie Kratz - ESSEC Business School, CREAR (France)
Abstract: The problem of finding methods to describe the extremal dependence among multiple time series has rapidly become attractive in recent years, due to the vast variety of fields where its practical implications are of interest. However, providing handy tools to assess such dependence is still challenging. An empirical method has been recently developed by Dacorogna and Cadena, where the authors provide a statistical approach to explore the dependence among extreme risks. The purpose is to develop further this problem from a theoretical point of view. The mathematical formalization that we propose involves the concept of concomitants of order statistics, widely studied in the literature. We focus on the asymptotic dependence between maxima of concomitants: Specifically, order a bivariate sequence of $n$ i.i.d. random variables $(X,Y)$ on the basis of the $X$-variable, and call the extreme set of the sequence $(X_n,Y_n)$ the subset of couples where the first component is one of the $k$ largest order statistics ($k$ fixed). Consider the vector formed by the maxima of the concomitants belonging to the extreme set and to its complementary set. We study how the bivariate extremal dependence of $(X,Y)$ influences the asymptotic joint distribution of the two maxima of concomitants. Revisiting a pivotal work, we propose an alternative way to tackle the problem, which allows us to consider the cases where upper tail dependence is present.