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Nonparametric Tests for Positive Quadrant Dependence

  • 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))

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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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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  1. Davidson, R. & Duclos, J.-Y., 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," G.R.E.Q.A.M. 98a14, Universite Aix-Marseille III.
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  13. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
  14. J. Pinquet, 1998. "Designing optimal bonus-malus systems from different types of claims," THEMA Working Papers 98-19, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  15. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
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