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Finite Representation of Quantile Sets for Multivariate Data via Vector Linear Programming (2303.15600v3)
Published 27 Mar 2023 in math.ST, math.OC, and stat.TH
Abstract: Empirical quantiles for finitely distributed univariate random variables can be obtained by solving a certain linear program. It is shown in this short note that multivariate empirical quantiles can be obtained in a very similar way by solving a vector linear program. This connection provides a new approach for computing Tukey depth regions and more general cone quantile sets.