Finite representation of quantile sets for multivariate data via vector linear programming

03/27/2023

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by   Andreas Löhne, et al.

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A well-known result states that empirical quantiles for finitely distributed univariate random variables can be obtained by solving a linear program. We show 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.