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

Authors:
Olivier Scaillet
Affiliations:
HEC Genève and Swiss Finance Institute, Université de Genève, Bd Carl Vogt, 102, CH - 1211 Genève 4, Switzerland
Venue:
Journal of Multivariate Analysis
Year:
2007

Citing 5
Cited 3

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Goodness-of-fit tests for copulas

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Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
An Introduction to Copulas (Springer Series in Statistics)

An Introduction to Copulas (Springer Series in Statistics)

Testing for equality between two copulas

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Flexible modeling based on copulas in nonparametric median regression

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Some comments on goodness-of-fit tests for the parametric form of the copula based on L2-distances

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Abstract

We study a test statistic based 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 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.