Lift zonoid and barycentric representation on a Banach space with a cylinder measure

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• 作者：Alexei M. Kulik (1)
  Taras D. Tymoshkevych (2)
  
• 关键词：zonoid ; lift zonoid ; cylinder measure ; barycentric representation ; primary 60D05 ; secondary 28C20
• 刊名：Lithuanian Mathematical Journal
• 出版年：2013
• 出版时间：April 2013
• 年：2013
• 卷：53
• 期：2
• 页码：181-195
• 全文大小：176KB
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• 作者单位：Alexei M. Kulik (1)
  Taras D. Tymoshkevych (2)
  
  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Str. 3, 01601, Kyiv, Ukraine
  2. Taras Shevchenko National University of Kyiv, Academician Glushkov Ave. 4-e, 03127, Kyiv, Ukraine
  
• ISSN：1573-8825

文摘

We show that the lift zonoid concept for a probability measure on $ {{\mathbb{R}}^d} $ , introduced in [G.A. Koshevoy and K. Mosler, Zonoid trimming for multivariate distributions, Ann. Stat., 25(5):1998-017, 1997], naturally leads to a oneto-one representation of any interior point of the convex hull of the support of a continuous measure as the barycenter w.r.t. this measure of either a half-space or the whole space. We prove an infinite-dimensional generalization of this representation, which is based on the extension of the concept of lift zonoid for a cylindrical probability measure.