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Concentration of the empirical contours of Tukey’s halfspace depth

Presented by: 
Victor Brunel
Friday 22nd June 2018 - 10:00 to 11:00
INI Seminar Room 2
Tukey's halfspace depth has attracted much interest in data analysis, because it is a natural way of measuring the notion of depth relative to a cloud of points or, more generally, to a probability measure. Given an i.i.d. sample, we investigate the concentration of upper level sets of the Tukey depth relative to that sample around their population version. We show that under some mild assumptions on the underlying probability measure, concentration occurs at a parametric rate and we deduce moment inequalities at that same rate. In a computational prospective, we study the concentration of a discretized version of the empirical upper level sets

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons