Nonparametric Tests for Positive Quadrant Dependence

Michel Denuit and Olivier Saillet
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Michel Denuit: UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE)
Olivier Saillet: UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES)
Authors registered in the RePEc Author Service: Olivier Scaillet

No 2001009, LIDAM Discussion Papers IRES from Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES)

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.

Keywords: Nonparametric; Stochastic Ordering; Positive Quadrant Dependence; Positive Orthant Dependence; Copula; Inequality Constraint Test; Risk Management; Loss Severity Distribution (search for similar items in EconPapers)
JEL-codes: C12 D81 G10 G21 G22 (search for similar items in EconPapers)
Pages: 26
Date: 2001-01-01, Revised 2001-04-01
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Citations: View citations in EconPapers (6)

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