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Bootstrapping L2-type statistics in copula density testing

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  • Rehbock Volker

Abstract

In this paper, we address the problem of testing the goodness of fit of a copula density function in the context of a d-dimensional i.i.d. sample by using a L2-type statistic. In extension to Fermanian [4], we propose to use a bootstrap approximation of the distribution of the test statistic. We show the validity of the bootstrap and perform a simulation study. Stochastic independence can be characterised in terms of the underlying copula and so we use the test as a test of independence.

Suggested Citation

  • Rehbock Volker, 2007. "Bootstrapping L2-type statistics in copula density testing," Statistics & Risk Modeling, De Gruyter, vol. 25(4), pages 333-347, October.
    • Handle: RePEc:bpj:strimo:v:25:y:2007:i:4/2007:p:15:n:5
    DOI: 10.1524/stnd.2007.0907
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    References listed on IDEAS

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    1. Neumann, Michael H. & Paparoditis, Efstathios, 2000. "On bootstrapping L2-type statistics in density testing," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 137-147, November.
    2. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    3. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
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