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Kernel Based Goodness-of-Fit Test for Copulas with Fixed Smoothing Parameters

FAME Research Paper No. 145

17 Pages Posted: 13 Sep 2005  

O. Scaillet

University of Geneva GSEM and GFRI; Swiss Finance Institute

Date Written: September 2005


We study a test statistic on the integrated squared difference between a kernel estimator of the copula density and a kernel smoothed estimator of the parametric copula density. We show for fixed smoothing parameters that the test is consistent and that the asymptotic properties are driven by a U-statistic of order 4 with degeneracy of order 3. For practical implementation we suggest to compute the critical values through a semiparametric bootstrap. Monte Carlo results show that the bootstrap procedure performs well in small samples. In particular size and power are less sensitive to smoothing parameter choice than they are under the asymptotic approximation obtained for a vanishing bandwidth.

Keywords: Nonparametric, Copula density, Goodness-of-fit test, U-statistic

JEL Classification: C12, D18, G10, G21, G22

Suggested Citation

Scaillet , O., Kernel Based Goodness-of-Fit Test for Copulas with Fixed Smoothing Parameters (September 2005). FAME Research Paper No. 145. Available at SSRN: or

Olivier Scaillet (Contact Author)

University of Geneva GSEM and GFRI ( email )

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Geneva 4, 1211
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Swiss Finance Institute

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