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Nonparametric Tests for Positive Quadrant Dependence

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Author Info
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))

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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.

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Publisher Info
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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Related research
Keywords: Nonparametric; Stochastic Ordering; Positive Quadrant Dependence; Positive Orthant Dependence; Copula; Inequality Constraint Test; Risk Management; Loss Severity Distribution;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
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; Mortgages
G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    Other versions:
  9. 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. [Downloadable!]
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  11. 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. [Downloadable!] (restricted)
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  14. Klugman, Stuart A. & Parsa, Rahul, 1999. "Fitting bivariate loss distributions with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 139-148, March. [Downloadable!] (restricted)
  15. Denuit, Michel & Dhaene, Jan & Ribas, Carmen, 2001. "Does positive dependence between individual risks increase stop-loss premiums?," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 305-308, June. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Kaïs Dachraoui & Georges Dionne, 2004. "Conditions Ensuring the Separability of Asset Demand for All Risk-Averse Investors," Cahiers de recherche 0411, CIRPEE. [Downloadable!]
  2. Lee & Myoung-jae, 2004. "Monotonicity Conditions and Inequality Imputation for Sample Selection and Non-Response Problems," Econometric Society 2004 Australasian Meetings 93, Econometric Society. [Downloadable!]
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