Nonparametric Tests for Positive Quadrant Dependence
AbstractWe 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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Bibliographic InfoPaper 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.
Date of creation: 01 Jan 2001
Date of revision: 01 Apr 2001
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 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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