# Estimation of copulas via Maximum Mean Discrepancy

arXiv: https://arxiv.org/abs/2010.00408 · HTML: https://mlsanity.com/paper/2010.00408/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Variance-Aware Estimation of Kernel Mean Embedding](https://mlsanity.com/paper/2210.06672/) (2022)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [Clustering Market Regimes using the Wasserstein Distance](https://mlsanity.com/paper/2110.11848/) (2021)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)
- [Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Data](https://mlsanity.com/paper/2505.08698/) (2025)

## Abstract (arXiv)

This paper deals with robust inference for parametric copula models. Estimation using Canonical Maximum Likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the Maximum Mean Discrepancy (MMD) principle. We derive non-asymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on [0,1]d, as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available.