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