# Bivariate vine copula based regression, bivariate level and quantile curves

arXiv: https://arxiv.org/abs/2205.02557 · HTML: https://mlsanity.com/paper/2205.02557/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 61 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 10 of 10)

- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Prediction based on conditional distributions of vine copulas](https://mlsanity.com/paper/1807.08429/) (2018)
- [Probit transformation for kernel density estimation on the unit interval](https://mlsanity.com/paper/1303.4121/) (2013)
- [D-vine copula based quantile regression](https://mlsanity.com/paper/1510.04161/) (2015)
- [Nonparametric C- and D-vine based quantile regression](https://mlsanity.com/paper/2102.04873/) (2021)
- [D-vine quantile regression with discrete variables](https://mlsanity.com/paper/1705.08310/) (2017)
- [Vector Quantile Regression: An Optimal Transport Approach](https://mlsanity.com/paper/1406.4643/) (2014)
- [Model distances for vine copulas in high dimensions](https://mlsanity.com/paper/1510.03671/) (2015)
- [Multivariate Confidence Intervals](https://mlsanity.com/paper/1701.05763/) (2017)
- [Testing the simplifying assumption in high-dimensional vine copulas](https://mlsanity.com/paper/1706.02338/) (2017)

## Built on by (most cited first, 1 of 1)

- [Assessing univariate and bivariate risks of late-frost and drought using vine copulas: A historical study for Bavaria](https://mlsanity.com/paper/2310.10324/) (2023)

## Abstract (arXiv)

The statistical analysis of univariate quantiles is a well developed research topic. However, there is a need for research in multivariate quantiles. We construct bivariate (conditional) quantiles using the level curves of vine copula based bivariate regression model. Vine copulas are graph theoretical models identified by a sequence of linked trees, which allow for separate modelling of marginal distributions and the dependence structure. We introduce a novel graph structure model (given by a tree sequence) specifically designed for a symmetric treatment of two responses in a predictive regression setting. We establish computational tractability of the model and a straight forward way of obtaining different conditional distributions. Using vine copulas the typical shortfalls of regression, as the need for transformations or interactions of predictors, collinearity or quantile crossings are avoided. We illustrate the copula based bivariate level curves for different copula distributions and show how they can be adjusted to form valid quantile curves. We apply our approach to weather measurements from Seoul, Korea. This data example emphasizes the benefits of the joint bivariate response modelling in contrast to two separate univariate regressions or by assuming conditional independence, for bivariate response data set in the presence of conditional dependence.