Lift expectations of random sets

Marc-Arthur Diaye, Gleb A. Koshevoy and Ilya Molchanov

Statistics & Probability Letters, 2019, vol. 145, issue C, 110-117

Abstract: It is known that the distribution of an integrable random vector ξ in Rd is uniquely determined by a (d+1)-dimensional convex body called the lift zonoid of ξ. This concept is generalised to define the lift expectation of random convex bodies. However, the unique identification property of distributions is lost; it is shown that the lift expectation uniquely identifies only one-dimensional distributions of the support function, and so different random convex bodies may share the same lift expectation. The extent of this nonuniqueness is analysed and it is related to the identification of random convex functions using only their one-dimensional marginals. Applications to construction of depth-trimmed regions and partial ordering of random convex bodies are also mentioned.

Keywords: Random set; Selection expectation; Lift zonoid; Support function; Risk measure; Outlier (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.08.015

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