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

机译:使用圆柱体量度在Banach空间上提升zonoid和重心表示

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We show that the lift zonoid concept for a probability measure on Rd, introduced in [G.A. Koshevoy and K. Mosler, Zonoid trimming for multivariate distributions, Ann. Stat., 25(5):1998–2017, 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.
机译:我们展示了在[G.A. Koshevoy和K.Mosler,针对多态分布的Zonoid修整,Ann。 Stat。,25(5):1998–2017,1997],自然得出一对一的表示,即连续测量的支撑的凸包的任何内部点作为重心w.r.t.。半空间或整个空间的度量。我们证明了这种表示形式的无穷维概括,它是基于圆柱概率测度的提升带样概念的扩展。

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