Authors: Gather, Ursula
Kwiecien, Robert
Title: Jensen's inequality for the Tukey median
Language (ISO): en
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).
Subject Headings: Jensen's inequality
Multivariate median
Robustness
Tukey depth
URI: http://hdl.handle.net/2003/24309
http://dx.doi.org/10.17877/DE290R-264
Issue Date: 2007-05-25T10:39:02Z
Appears in Collections:Sonderforschungsbereich (SFB) 475

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