Journal ArticleDOI
The Lorenz zonotope and multivariate majorizations
TLDR
In this article, a geometric approach to order row stochastic matrices is presented, where a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced.Abstract:
The distribution of d commodities among n individuals is described by an n×d row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The Lorenz zonotope is a convex polytope. The inclusion of Lorenz zonotopes defines an ordering between row stochastic matrices, which is a multivariate majorization. For a cone in nonnegative d-space, a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced. We study this class of orderings and establish equivalence with known majorizations. It is provided a finite set of inequalities to which the ordering is equivalent.read more
Citations
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Journal ArticleDOI
Asymptotic Properties for a Class of Partially Identified Models
TL;DR: In this paper, the authors show that the Hausdorff distance between the estimator and the population identification region, when properly normalized by square n, converges in distribution to the supremum of a Gaussian process whose covariance kernel depends on parameters of the population identificaiton region.
Journal ArticleDOI
Multidimensional Poverty and Inequality
Rolf Aaberge,Andrea Brandolini +1 more
TL;DR: In this article, the authors examine different approaches to the measurement of multidimensional inequality and poverty and highlight areas for future research and offer some guidance on how to use multi-dimensional methods in empirical and policy-oriented applications.
Journal ArticleDOI
The impossibility of a Paretian egalitarian
Marc Fleurbaey,Alain Trannoy +1 more
TL;DR: This paper studies the case of multiple goods (without using prices as a means to come back to one dimension), and shows that many results of the one-dimensional setting carry over to the multidimensional case when individuals are assumed to have identical preferences.
Book ChapterDOI
Multidimensional Poverty and Inequality
Rolf Aaberge,Andrea Brandolini +1 more
TL;DR: In this paper, the authors examine different approaches to the measurement of multidimensional inequality and poverty and highlight areas for future research and offer some guidance on how to use multi-dimensional methods in empirical and policy-oriented applications.
Journal ArticleDOI
Multivariate convex orderings, dependence, and stochastic equality
TL;DR: In this article, the authors consider the convex ordering for random vectors and some weaker versions of it, like convex orderings for linear combinations of random variables, and establish conditions of stochastic equality for the random vectors that are ordered by one of these orderings.
References
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Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
Journal ArticleDOI
On the Measurement of Inequality
TL;DR: In this paper, the problem of comparing two frequency distributions f(u) of an attribute y which for convenience I shall refer to as income is defined as a risk in the theory of decision-making under uncertainty.
Journal ArticleDOI
The Measurement and Decomposition of Multi-Dimensional Inequality
TL;DR: JSTOR as mentioned in this paper is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship, which is used to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources.
Book
Majorization and the Lorenz Order: A Brief Introduction
TL;DR: The Lorenz order in the space of distribution functions was introduced in this paper for IR and has been applied in many applications, e.g., genetic selection, genetic selection and large interactions.