Testing for Concordance Ordering

FAME Research Paper No. 41

42 Pages Posted: 24 May 2002

See all articles by Ana C. Cebrian

Ana C. Cebrian

University of Zaragoza

Michel Denuit

Catholic University of Louvain

O. Scaillet

Swiss Finance Institute - University of Geneva

Date Written: March 2002

Abstract

We propose inference tools to analyse the ordering of concordance of random vectors. The analysis in the bivariate case relies on tests for upper and lower quadrant dominance of the true distribution by a parametric or semiparametric model, i.e. for a parametric or semiparametric model to give a probability that two variables are simultaneously small or large at least as great as it would be were they left unspecified. Tests for its generalisation in higher dimensions, namely analysed. The parametric and semiparametric setting are based on the copula representation for multivariate distribution, which allows for disentangling behaviour of margins and dependence structure. We propose two types of testing procedures for each setting. The first procedure is based on a formulation of the dominance concepts in terms of values taken by random variables, while the second procedure is based on a formulation in terms of probability levels. For each formulation a distance test and an intersection-union test for inequality constraints are developed depending on the definition of null and alternative hypotheses. An empirical illustration is given for US insurance claim data.

Keywords: Nonparametric, Concordance Ordering, Quadrant Dominance, Orthant Dominance, Copula, Inequality Constraint Tests, Risk Management, Loss Severity Distribution

JEL Classification: C12, D81, G10, G21, G22

Suggested Citation

Cebrian, Ana Carmen and Denuit, Michel and Scaillet, Olivier, Testing for Concordance Ordering (March 2002). FAME Research Paper No. 41, Available at SSRN: https://ssrn.com/abstract=307662 or http://dx.doi.org/10.2139/ssrn.307662

Ana Carmen Cebrian

University of Zaragoza ( email )

Gran Via 2
Zaragoza, 50005
Spain

Michel Denuit

Catholic University of Louvain ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

Olivier Scaillet (Contact Author)

Swiss Finance Institute - University of Geneva ( email )

Geneva
Switzerland