p-norm bounds on the expectation of the maximum of a possibly dependent sample
type: Item
instance of: scholarly article
title: p-norm bounds on the expectation of the maximum of a possibly dependent sample
zbMATH Open document ID: 0584.62072
DOI: 10.1016/0047-259X(85)90087-9
author: Barry C. Arnold
published in: Journal of Multivariate Analysis
publication date: 1985-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,...,X_ n\) be identically distributed possibly dependent random variables with finite pth absolute moment assumed without loss of generality to be equal to 1. Denote the order statistics by \(X_{1:n},X_{2:n},...,X_{n:n}\). Bounds are derived for \(E(X_{n:n})\) when it is assumed that the \(X_ i's\) are (i) arbitrarily dependent and (ii) independent. The effect of assuming a symmetric common distribution for the \(X_ i's\) is discussed. Analogous bounds are described for the expected range of the sample. Bounds on expectations of general linear combinations of order statistics are described in the independent case.
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 3936231
zbMATH Keywords: p-norm bounds
zbMATH Keywords: maximal dependence
zbMATH Keywords: maximum of dependent sample
zbMATH Keywords: order statistics
zbMATH Keywords: independent
zbMATH Keywords: symmetric common distribution
zbMATH Keywords: expected range
zbMATH Keywords: expectations of general linear combinations of order statistics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3936231