Testing the simplifying assumption in high-dimensional vine copulas

Kurz, Malte S. und Spanhel, Fabian (2022): Testing the simplifying assumption in high-dimensional vine copulas. In: Electronic Journal of Statistics, Bd. 16, Nr. 2: S. 5226-5276

Abstract

Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observa-tions and check constraints on high-dimensional distributions. So far, cor-responding tests have been limited to single conditional copulas with a low-dimensional set of conditioning variables. We propose a novel testing procedure that is computationally feasible for high-dimensional data sets and that exhibits a power that decreases only slightly with the dimension. By discretizing the support of the conditioning variables and incorporating a penalty in the test statistic, we mitigate the curse of dimensionality by looking for the possibly strongest deviation from the simplifying assump-tion. The use of a decision tree renders the test computationally feasible for large dimensions. We derive the asymptotic distribution of the test and analyze its finite sample performance in an extensive simulation study. An application of the test to four real data sets is provided.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Statistik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1935-7524
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 431701914