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

Authors:
Axel Bücher;Holger Dette
Affiliations:
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany;Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany
Venue:
Journal of Multivariate Analysis
Year:
2010

Citing 4
Cited 0

Goodness-of-fit tests for copulas

Journal of Multivariate Analysis
An Introduction to Copulas (Springer Series in Statistics)

An Introduction to Copulas (Springer Series in Statistics)
Note: Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters

Journal of Multivariate Analysis
A goodness of fit test for copulas based on Rosenblatt's transformation

Computational Statistics & Data Analysis

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Abstract

In a recent paper Fermanian (2005) [9] studied a goodness-of-fit test for the parametric form of a copula, which is based on an L^2-distance between a parametric and a nonparametric estimate of the copula density. In the present paper we investigate the asymptotic properties of the proposed test statistic under fixed alternatives. We also study the impact of different estimates for the parameters of the finite-dimensional family of copulas specified by the null hypothesis and illustrate the performance of a parametric bootstrap procedure for the approximation of the critical values.