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Nonparametric Tests for Positive Quadrant Dependence

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  • Michel Denuit

Abstract

We consider distributional free inference to test for positive quadrant dependence, that is, 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 generalization to higher dimensions, namely positive orthant dependence, are also analyzed. 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 for time-dependent data. An empirical illustration is given for U.S. insurance claim data, where we discuss practical implications for the design of reinsurance treaties. Another application concerns detection of positive quadrant dependence between the HFR and CSFB-Tremont market neutral hedge fund indices and the S&P 500 index. Copyright 2004, Oxford University Press.

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  • Michel Denuit, 2004. "Nonparametric Tests for Positive Quadrant Dependence," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 422-450.
    • Handle: RePEc:oup:jfinec:v:2:y:2004:i:3:p:422-450
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbh017
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    Cited by:

    1. Gijbels, Irène & Sznajder, Dominik, 2013. "Testing tail monotonicity by constrained copula estimation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 338-351.
    2. 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.
    3. Mullahy, John, 2024. "Analyzing health outcomes measured as bounded counts," Journal of Health Economics, Elsevier, vol. 95(C).
    4. 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;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 139-157, July.
    5. Ortega, Eva-María & Escudero, Laureano F., 2010. "On expected utility for financial insurance portfolios with stochastic dependencies," European Journal of Operational Research, Elsevier, vol. 200(1), pages 181-186, January.
    6. Olivier Cabrignac & Arthur Charpentier & Ewen Gallic, 2020. "Modeling Joint Lives within Families," Working Papers halshs-02871927, HAL.
    7. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    8. Ledwina, Teresa & Wyłupek, Grzegorz, 2014. "Validation of positive quadrant dependence," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 38-47.
    9. Guo, Xu & Li, Jingyuan, 2016. "Confidence band for expectation dependence with applications," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 141-149.
    10. Gordon Anderson & Kinda Hachem, 2013. "Institutions and Economic Outcomes: A Dominance-Based Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 164-182, January.
    11. Georges Dionne & Jingyuan Li & Cédric Okou, 2024. "An alternative representation of the C-CAPM with higher-order risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 49(2), pages 194-233, September.
    12. Lei Jiang & Esfandiar Maasoumi & Jiening Pan & Ke Wu, 2018. "A test of general asymmetric dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 1026-1043, November.
    13. Jeffrey Racine, 2015. "Mixed data kernel copulas," Empirical Economics, Springer, vol. 48(1), pages 37-59, February.
    14. 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.
    15. Zongwu Cai & Xian Wang, 2014. "Selection of Mixed Copula Model via Penalized Likelihood," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 788-801, June.
    16. Shen, Xiaojing & Zhu, Yunmin & Song, Lixin, 2008. "Linear B-spline copulas with applications to nonparametric estimation of copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3806-3819, March.
    17. 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.
    18. Holzer, Jorge & Olson, Lars J., 2021. "Precautionary buffers and stochastic dependence in environmental policy," Journal of Environmental Economics and Management, Elsevier, vol. 106(C).
    19. Kais Dachraoui & Georges Dionne, 2007. "Conditions Ensuring the Decomposition of Asset Demand for All Risk-Averse Investors," The European Journal of Finance, Taylor & Francis Journals, vol. 13(5), pages 397-404.
    20. Xuehu Zhu & Xu Guo & Lu Lin & Lixing Zhu, 2016. "Testing for positive expectation dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 135-153, February.
    21. 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.
    22. Kyungchul Song, 2009. "Testing Predictive Ability and Power Robustification," PIER Working Paper Archive 09-035, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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