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Testing for Concordance Ordering

Published online by Cambridge University Press:  17 April 2015

Ana C. Cebrián ,
Michel Denuit  and
Olivier Scaillet
Ana C. Cebrián
Affiliation:
Dpto. Métodos Estadisticos. Ed. Matematicas, Facultad de Ciencias, Universidad de Zaragoza, CP. Cerbuna, 12 S-Zaragoza 50009, Spain, E-mail: acebrian@unizar.es
Michel Denuit
Affiliation:
Institut de Statistique, Université Catholique de Louvain, Voie du Roman Pays, 20 B-1348 Louvain-la-Neuve, Belgium, E-mail: denuit@stat.ucl.ac.be
Olivier Scaillet
Affiliation:
HEC Genéve and FAME, Université de Genéve, Bd Carl Vogt, 102 CH-1211 Genéve 4, Suisse, E-mail: olivier.scaillet@hec.unige.ch
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Abstract

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We propose inference tools to analyse the concordance (or correlation) order 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 joint lower and upper orthant dominance, are also analysed. The parametric and semiparametric settings are based on the copula representation for multivariate distribution, which allows for disentangling behaviour of margins and dependence structure. 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

NonparametricConcordance (Correlation) OrderQuadrant DominanceOrthant DominanceCopulaInequality Constraint TestsRisk ManagementLoss Severity Distribution
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 1 , May 2004 , pp. 151 - 173
Copyright
Copyright © ASTIN Bulletin 2004

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