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August 2015 Asymptotic total variation tests for copulas
Jean-David Fermanian, Dragan Radulović, Marten Wegkamp
Bernoulli 21(3): 1911-1945 (August 2015). DOI: 10.3150/14-BEJ632


We propose a new platform of goodness-of-fit tests for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The standard Kolmogorov–Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by orthants is extended by test statistics based on the empirical copula process indexed by families of $L_{n}$ disjoint boxes, with $L_{n}$ slowly tending to infinity. Although the underlying empirical process does not converge, the critical values of our new test statistics can be consistently estimated by nonparametric bootstrap techniques, under simple or composite null assumptions. We implemented a particular example of these tests and our simulations confirm that the power of the new procedure is oftentimes higher than the power of the standard Kolmogorov–Smirnov or the Cramér–von Mises tests for copulas.


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Jean-David Fermanian. Dragan Radulović. Marten Wegkamp. "Asymptotic total variation tests for copulas." Bernoulli 21 (3) 1911 - 1945, August 2015.


Received: 1 November 2012; Revised: 1 April 2014; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1331.62282
MathSciNet: MR3352066
Digital Object Identifier: 10.3150/14-BEJ632

Keywords: bootstrap , copula , empirical copula process , Goodness-of-fit test , weak convergence

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 3 • August 2015
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