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math.ST2014
Monge-Kantorovich Depth, Quantiles, Ranks, and Signs
Victor Chernozhukov, Alfred Galichon, Marc Hallin +1
We propose new concepts of statistical depth, multivariate quantiles, ranks and signs, based on canonical transportation maps between a distribution of interest on and a refe…
math.ST2014
Central Limit Theorems and Bootstrap in High Dimensions
Victor Chernozhukov, Denis Chetverikov, Kengo Kato
This paper derives central limit and bootstrap theorems for probabilities that sums of centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets. Specif…