Lift expectations of random sets

Publication date: Available online 8 September 2018Source: Statistics & Probability LettersAuthor(s): Marc-Arthur Diaye, Gleb A. Koshevoy, Ilya MolchanovAbstractIt 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.

Source: Statistics and Probability Letters - September 9, 2018 Category: Statistics Source Type: research