Estimation of copulas via Maximum Mean Discrepancy

  title={Estimation of copulas via Maximum Mean Discrepancy},
  author={Pierre Alquier and Badr-Eddine Ch'erief-Abdellatif and A. Derumigny and Jean-David Fermanian},
  journal={Journal of the American Statistical Association},
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… 

Figures and Tables from this paper

Implicit Generative Copulas
This paper proposes a flexible, yet conceptually simple alternative based on implicit generative neural networks that can obtain samples from the high-dimensional copula distribution without relying on parametric assumptions or the need to find a suitable tree structure.
Clustering Market Regimes Using the Wasserstein Distance
An unsupervised learning algorithm for clustering financial time-series into a suitable number of temporal segments (market regimes) and develops a robust algorithm that automates the process of classifying market regimes.
Sample from copula: a COPPY module
COPPY is a library that provides a range of random vector generation vector for copulae and helps to promote the dependence modeling with copula in Python.


Robust Estimation of Bivariate Copulas
A bounded-bias robust estimator that is corrected for consistency by means of indirect inference is proposed and in a simulation study it is shown that the robust estimators outperform the popular approaches.
Robust Fits for Copula Models
It is shown that there is a robust estimator improving over the MLE and able to capture the correct strength of dependence of the data, despite the contamination percentual and location, and the sample size.
Semiparametric estimation in copula models
The author recalls the limiting behaviour of the empirical copula process and applies it to prove some asymptotic properties of a minimum distance estimator for a Euclidean parameter in a copula
Robust estimators and tests for bivariate copulas based on likelihood depth
Statistical Inference for Generative Models with Maximum Mean Discrepancy
Theoretical properties of a class of minimum distance estimators for intractable generative models, that is, statistical models for which the likelihood is intracted, but simulation is cheap, are studied, showing that they are consistent, asymptotically normal and robust to model misspecification.
MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy
A pseudo-likelihood based on the Maximum Mean Discrepancy, defined via an embedding of probability distributions into a reproducing kernel Hilbert space is built, and it is shown that this MMD-Bayes posterior is consistent and robust to model misspecification.
Subsampling (weighted smooth) empirical copula processes
A new method for estimation and model selection:$$\rho $$ρ-estimation
The aim of this paper is to present a new estimation procedure that can be applied in various statistical frameworks including density and regression and which leads to both robust and optimal (or
Weak convergence of the empirical copula process with respect to weighted metrics
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak