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November 2020 Goodness-of-fit testing for copulas: A distribution-free approach
Sami Umut Can, John H.J. Einmahl, Roger J.A. Laeven
Bernoulli 26(4): 3163-3190 (November 2020). DOI: 10.3150/20-BEJ1219

Abstract

Consider a random sample from a continuous multivariate distribution function $F$ with copula $C$. In order to test the null hypothesis that $C$ belongs to a certain parametric family, we construct an empirical process on the unit hypercube that converges weakly to a standard Wiener process under the null hypothesis. This process can therefore serve as a ‘tests generator’ for asymptotically distribution-free goodness-of-fit testing of copula families. We also prove maximal sensitivity of this process to contiguous alternatives. Finally, we demonstrate through a Monte Carlo simulation study that our approach has excellent finite-sample performance, and we illustrate its applicability with a data analysis.

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Sami Umut Can. John H.J. Einmahl. Roger J.A. Laeven. "Goodness-of-fit testing for copulas: A distribution-free approach." Bernoulli 26 (4) 3163 - 3190, November 2020. https://doi.org/10.3150/20-BEJ1219

Information

Received: 1 April 2019; Revised: 1 March 2020; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256172
MathSciNet: MR4140541
Digital Object Identifier: 10.3150/20-BEJ1219

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 4 • November 2020
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