# Estimating Non-Simplified Vine Copulas Using Penalized Splines

arXiv: https://arxiv.org/abs/1603.01424 · HTML: https://mlsanity.com/paper/1603.01424/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2016.

## Built on by (most cited first, 2 of 2)

- [Pair Programming with Large Language Models for Sampling and Estimation of Copulas](https://mlsanity.com/paper/2303.18116/) (2023)
- [Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactions](https://mlsanity.com/paper/2605.03061/) (2026)

## Abstract (arXiv)

Vine copulas (or pair-copula constructions) have become an important tool for high-dimensional dependence modeling. Typically, so called simplified vine copula models are estimated where bivariate conditional copulas are approximated by bivariate unconditional copulas. We present the first non-parametric estimator of a non-simplified vine copula that allows for varying conditional copulas using penalized hierarchical B-splines. Throughout the vine copula, we test for the simplifying assumption in each edge, establishing a data-driven non-simplified vine copula estimator. To overcome the curse of dimensionality, we approximate conditional copulas with more than one conditioning argument by a conditional copula with the first principal component as conditioning argument. An extensive simulation study is conducted, showing a substantial improvement in the out-of-sample Kullback-Leibler divergence if the null hypothesis of a simplified vine copula can be rejected. We apply our method to the famous uranium data and present a classification of an eye state data set, demonstrating the potential benefit that can be achieved when conditional copulas are modeled.