Jensen's inequality for the Tukey median

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Date

2007-05-25T10:39:02Z

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Abstract

Jensen's inequality states for a random variable X with values in Rd and existing expectation and for any convex function f : R^d -> R, that f(E(X)) <= E(f(X)). We prove an analogous inequality, where the expectation operator is replaced by the halfspace-median-operator (or Tukey-median-operator).

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Keywords

Jensen's inequality, Multivariate median, Robustness, Tukey depth

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