Lift expectations of random sets

Augmenter les attentes concernant les ensembles aléatoires

Marc-Arthur Diaye (), Gleb Koshevoy and Ilya Molchanov
Additional contact information
Marc-Arthur Diaye: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

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: 2019-02
Note: View the original document on HAL open archive server: https://cnrs.hal.science/hal-03897964v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Statistics and Probability Letters, 2019, 145, pp.110-117. ⟨10.1016/j.spl.2018.08.015⟩

Downloads: (external link)
https://cnrs.hal.science/hal-03897964v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03897964

DOI: 10.1016/j.spl.2018.08.015

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().