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Nonparametric Tests for Positive Quadrant Dependence

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  • DENUIT, Michel

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE))

  • SAILLET, Olivier

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

Abstract

We consider distributional free inference to test for positive quadrant dependence, i.e. for the probability that two variables are simultaneously small (or) large being at least as great as it would be were they dependent. Tests for its generalisation in higher dimensions, namely positive orthant dependences, are also analysed. We propose two types of testing procedures. The first procedure is based on the specification of the dependence concepts in terms of distribution functions, while the second procedure exploits the copula representation. For each specification 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 and Danish insurance claim data. Practical implications for the design of reinsurance treaties are also discussed.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 2001009.

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Length: 26
Date of creation: 01 Jan 2001
Date of revision: 01 Apr 2001
Handle: RePEc:ctl:louvir:2001009

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Related research

Keywords: Nonparametric; Stochastic Ordering; Positive Quadrant Dependence; Positive Orthant Dependence; Copula; Inequality Constraint Test; Risk Management; Loss Severity Distribution;

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Cited by:
  1. Lee & Myoung-jae, 2004. "Monotonicity Conditions and Inequality Imputation for Sample Selection and Non-Response Problems," Econometric Society 2004 Australasian Meetings, Econometric Society 93, Econometric Society.
  2. Garcia, René & Tsafack, Georges, 2011. "Dependence structure and extreme comovements in international equity and bond markets," Journal of Banking & Finance, Elsevier, Elsevier, vol. 35(8), pages 1954-1970, August.
  3. Genest, Christian & Segers, Johan, 2010. "On the covariance of the asymptotic empirical copula process," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 101(8), pages 1837-1845, September.
  4. Kaïs Dachraoui & Georges Dionne, 2004. "Conditions Ensuring the Separability of Asset Demand for All Risk-Averse Investors," Cahiers de recherche, CIRPEE 0411, CIRPEE.
  5. Ranoua Bouchouicha, 2010. "Dépendance entre risques extrêmes : Application aux Hedge Funds," Working Papers, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure 1013, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  6. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
  7. Laureano Escudero & Eva-María Ortega, 2009. "How retention levels influence the variability of the total risk under reinsurance," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 17(1), pages 139-157, July.

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