Multivariate stochastic dominance with fixed dependence structure
type: Item
instance of: scholarly article
title: Multivariate stochastic dominance with fixed dependence structure
zbMATH Open document ID: 0655.90002
DOI: 10.1016/0167-6377(88)90038-7
author: Marco Scarsini
published in: Operations Research Letters
publication date: 1988-01-01T00:00:00Z
review text: A stochastic dominance relation is a partial ordering of probability distributions given by \[ (*)\quad \int_{{\mathcal X}}\phi (x) dF(x)\quad \geq \quad \int_{{\mathcal X}}\phi (x) dG(x)\quad for\quad all\quad \phi \in \Phi \] where F and G denote probability measures and \(\Phi\) is a given set of real-valued functions. When \({\mathcal X}\) is the real line and \(\Phi\) is, e.g., the set of all increasing, all concave, or all completely monotone functions, simple conditions are well-known which are necessary and sufficient for (*). Further, when \({\mathcal X}={\mathbb{R}}^ d \)and F as well as G are distributions of d independent random variables (*) is equivalent to conditions on the univariate marginal distributions only. The present contribution extends one of the latter results: Let F and G be distributions of dependent variables which have the same dependence structure in terms of their copula, and let \(\Phi\) be the set of all componentwise increasing measurable functions \({\mathbb{R}}\) \(d\to {\mathbb{R}}\). Then, (*) if and only if the usual univariate dominance conditions hold for every marginal.
Mathematics Subject Classification ID: 91B06
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 4070581
zbMATH Keywords: stochastic dominance
zbMATH Keywords: partial ordering of probability distributions
reviewed by: Karl Mosler
MaRDI profile type: Publication
full work available at URL: 0167-6377(88)90038-7
OpenAlex ID: W2032982241
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description: scientific article; zbMATH DE number 4070581