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Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters

Published in Journal of Multivariate Analysis. 2007, vol. 98, no. 3, p. 533-543
Abstract We study a test statistic based on the integrated squared difference between a kernel es- timator 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 1. 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 NonparametricCopula densityGoodness-of-fit testU- statistic
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Research group Geneva Finance Research Institute (GFRI)
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SCAILLET, Olivier. Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters. In: Journal of Multivariate Analysis, 2007, vol. 98, n° 3, p. 533-543. https://archive-ouverte.unige.ch/unige:79878

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Deposited on : 2016-01-22

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