Resumen/Abstract
Statistical depth is a non-parametric tool applicable to multivariate and non-Euclidean data, whose goal is a reasonable generalisation of quantiles to multivariate and more exotic datasets. We discuss the halfspace depth, arguably the most crucial depth in statistics. J. W. Tukey proposed that depth in 1975; its rigorous investigation started in the 1990s, and still, an abundance of open problems stimulates research in the area. We present surprising links of the halfspace depth with well-studied concepts from convex geometry. Using these relations, we partially resolve several open problems concerning depth. In particular, we resolve the 30-year-old characterisation conjecture, asking whether two different measures can correspond to the same halfspace depth.
Curriculum ponente
Stanislav Nagy obtained his PhD in 2016 from KU Leuven (Belgium) in Mathematics and Charles University (Czech Republic) in Probability and Mathematical Statistics. His research focuses on nonparametric and robust analysis of multivariate and functional data, especially in combination with approaches from probability, geometry, or functional analysis. He has co-authored more than 30 research articles and co-edited two books of conference proceedings. Currently, he works as an Assistant Professor at the Department of Probability and Mathematical Statistics of Charles University in Prague.
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