A regularized goodness-of-fit test for copulas

Genest, Christian; Huang, Wanling; Dufour, Jean-Marie

Journal de la société française de statistique, Tome 154 (2013) no. 1, pp. 64-77.

Les auteurs proposent une statistique de type Anderson–Darling pour tester l’ajustement d’une copule. Ils déterminent la loi limite de la statistique sous l’hypothèse nulle. Puisque cette loi dépend de la valeur inconnue du paramètre de la copule, ils font appel à une approche par multiplicateurs pour le calcul du seuil du test. Ils évaluent la puissance du test par voie de simulation et trouvent qu’elle surpasse généralement celle du test de Cramér–von Mises fondé sur la distance entre la copule empirique et une estimation paramétrique de la copule convergente sous ${\mathscr{H}}_0$.

The authors propose an Anderson–Darling-type statistic for copula goodness-of-fit testing. They determine the asymptotic distribution of the statistic under the null hypothesis. As this distribution depends on the unknown value of the copula parameter, they call on a multiplier method to compute the $p$-value of the test. They assess the power of the test through simulations and find that it is generally superior to that of the Cramér–von Mises statistic based on the distance between the empirical copula and a consistent parametric copula estimate under ${\mathscr{H}}_0$.

Keywords: Anderson–Darling statistic, Cramér–von Mises statistic, empirical copula, Gaussian process, Monte Carlo study, Multiplier Central Limit Theorem, pseudo-observation, rank
Mot clés : statistique de Anderson–Darling, statistique de Cramér–von Mises, copule empirique, processus Gaussien, étude de Monte Carlo, théorème central limit à multiplicateurs, pseudo-observation, rang

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