# Testing the simplifying assumption in high-dimensional vine copulas

## TL;DR

This paper introduces a new computationally feasible test for the simplifying assumption in high-dimensional vine copulas, effectively handling large datasets and high dimensions with minimal power loss.

## Contribution

It proposes a novel testing procedure that discretizes conditioning variables and uses decision trees to detect deviations, overcoming the curse of dimensionality.

## Key findings

- Test maintains high power in high dimensions
- Method is computationally feasible for large datasets
- Effective in real data applications

## Abstract

Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observations and check constraints on high-dimensional distributions. So far, corresponding 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 assumption. 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.