Ordering Functions of Random Vectors, with Application to Partial Sums

Michel M. Denuit () and Mhamed Mesfioui
Additional contact information
Michel M. Denuit: Université Catholique de Louvain
Mhamed Mesfioui: Université du Québec à Trois-Rivières

Journal of Theoretical Probability, 2013, vol. 26, issue 2, 474-479

Abstract: Abstract It is known that the sums of the components of two random vectors (X 1,X 2,…,X n ) and (Y 1,Y 2,…,Y n ) ordered in the multivariate (s 1,s 2,…,s n )-increasing convex order are ordered in the univariate (s 1+s 2+⋯+s n )-increasing convex order. More generally, real-valued functions of (X 1,X 2,…,X n ) and (Y 1,Y 2,…,Y n ) are ordered in the same sense as long as these functions possess some specified non-negative cross-derivatives. This note extends these results to multivariate functions. In particular, we consider vectors of partial sums (S 1,S 2,…,S n ) and (T 1,T 2,…,T n ) where S j =X 1+⋯+X j and T j =Y 1+⋯+Y j and we show that these random vectors are ordered in the multivariate (s 1,s 1+s 2,…,s 1+⋯+s n )-increasing convex order. The consequences of these general results for the upper orthant order and the orthant convex order are discussed.

Keywords: Multivariate increasing convex order of higher degree; Upper orthant (convex) order; Stochastic recursive equations; 60E15 (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-012-0402-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jotpro:v:26:y:2013:i:2:d:10.1007_s10959-012-0402-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-012-0402-y

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().