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Nonparametric Tests for Positive Quadrant Dependence

Author

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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.

Suggested Citation

  • DENUIT, Michel & SAILLET, Olivier, 2001. "Nonparametric Tests for Positive Quadrant Dependence," LIDAM Discussion Papers IRES 2001009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 01 Apr 2001.
    • Handle: RePEc:ctl:louvir:2001009
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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 93, Econometric Society.
    2. Ranoua Bouchouicha, 2010. "Dépendance entre risques extrêmes : Application aux Hedge Funds," Working Papers 1013, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    3. Garcia, René & Tsafack, Georges, 2011. "Dependence structure and extreme comovements in international equity and bond markets," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1954-1970, August.
    4. 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.
    5. Kaïs Dachraoui & Georges Dionne, 2004. "Conditions Ensuring the Separability of Asset Demand for All Risk-Averse Investors," Cahiers de recherche 0411, CIRPEE.
    6. Genest, Christian & Segers, Johan, 2010. "On the covariance of the asymptotic empirical copula process," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1837-1845, September.

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    More about this item

    Keywords

    Nonparametric; Stochastic Ordering; Positive Quadrant Dependence; Positive Orthant Dependence; Copula; Inequality Constraint Test; Risk Management; Loss Severity Distribution;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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