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Nonparametric Tests Dependence For Positive Quadrant

Author

Listed:
  • Michel DENUIT

    (Université Catholique de Louvain)

  • Olivier SCAILLET

    (HEC-Université de Genève and FAME)

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 spcification 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

  • Michel DENUIT & Olivier SCAILLET, 2002. "Nonparametric Tests Dependence For Positive Quadrant," FAME Research Paper Series rp44, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp44
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    Cited by:

    1. Fermanian, Jean-David & Scaillet, Olivier, 2003. "Nonparametric estimation of copulas for time series," Working Papers unige:41797, University of Geneva, Geneva School of Economics and Management.

    More about this item

    Keywords

    Nonparametric; Stochastic Ordering; Positive Quadrant Dependence; Positive Orthant Dependence; Copula; Inequality constraint; 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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