Concentration bounds for the empirical angular measure with statistical learning applications. (arXiv:2104.03966v2 [math.ST] UPDATED)

The angular measure on the unit sphere characterizes the first-order
dependence structure of the components of a random vector in extreme regions
and is defined in terms of standardized margins. Its statistical recovery is an
important step in learning problems involving observations far away from the
center. In the common situation that the components of the vector have
different distributions, the rank transformation offers a convenient and robust
way of standardizing data in order to build an empirical version of …

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