New properties of the orthant convex-type stochastic orders

J. M. Fernández-Ponce () and M. R. Rodríguez-Griñolo ()
Additional contact information
J. M. Fernández-Ponce: Universidad de Sevilla
M. R. Rodríguez-Griñolo: Universidad Pablo de Olavide

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 3, No 8, 618-637

Abstract: Abstract The orthant convex and concave orders have been studied in the literature as extensions of univariate variability orders. In this paper, new results are proposed for bivariate orthant convex-type orders between vectors. In particular, we prove that these orders cannot be considered as dependence orders since they fail to verify several desirable properties that any positive dependence order should satisfy. Among other results, the relationships between these orders under certain transformations are presented, as well as that the orthant convex orders between bivariate random vectors with the same means are sufficient conditions to order the corresponding covariances. We also show that establishing the upper orthant convex or lower orthant concave orders between two vectors in the same Fréchet class is not equivalent to establishing these orders between the corresponding copulas except when marginals are uniform distributions. Several examples related with concordance measures, such as Kendall’s tau and Spearman’s rho, are also given, as are results on mixture models.

Keywords: Concordance measures; Dependence stochastic orders; Mixture models; Orthant convex stochastic orders; 60E99; 60E05 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11749-017-0527-5 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:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0527-5

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/11749/PS2

DOI: 10.1007/s11749-017-0527-5

Access Statistics for this article

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Alfonso Gordaliza and Ana F. Militino

More articles in TEST: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().