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Testing for Concordance Ordering

Author

Listed:
  • Cebrián, Ana C.
  • Denuit, Michel
  • Scaillet, Olivier

Abstract

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.

Suggested Citation

  • Cebrián, Ana C. & Denuit, Michel & Scaillet, Olivier, 2004. "Testing for Concordance Ordering," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 151-173, May.
    • Handle: RePEc:cup:astinb:v:34:y:2004:i:01:p:151-173_01
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    Cited by:

    1. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    2. Zheng, Yanting & Yang, Jingping & Huang, Jianhua Z., 2011. "Approximation of bivariate copulas by patched bivariate Fréchet copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 246-256, March.
    3. Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering.
    4. Eduardo F. L. de Melo & Beatriz Vaz de Melo Mendes, 2009. "Local Estimation of Copula Based Value-at-Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 7(1), pages 29-50.
    5. Beatriz Vaz de Melo Mendes, 2005. "Computing Conditional VaR using Time-varying CopulasComputing Conditional VaR using Time-varying Copulas," Brazilian Review of Finance, Brazilian Society of Finance, vol. 3(2), pages 251-265.
    6. Jean-David Fermanian, 2003. "Goodness of Fit Tests for Copulas," Working Papers 2003-34, Center for Research in Economics and Statistics.
    7. Leena Kulkarni & Sanjeev Sabnis & Sujit K. Ghosh, 2022. "Parameter Estimation for Multi-state Coherent Series and Parallel Systems with Positively Quadrant Dependent Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 714-742, August.
    8. 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.

    More about this item

    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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