Minimum Copula Divergence for Robust Estimation

2025-02-24

AI Summary

To address the lack of robustness of classical maximum likelihood estimation (MLE) under model misspecification and heavy-tailed data, this paper proposes a copula-only robust estimation framework. The method introduces a family of α/β/γ-divergences specifically tailored to copulas and constructs the minimum copula divergence estimator (MCDE), which directly minimizes the divergence between a parametric copula and the empirical copula—bypassing marginal distribution modeling entirely. Theoretically, we establish bounded influence functions for MCDE under Archimedean and elliptical copula families, ensuring strong robustness. Numerical experiments demonstrate that MCDE consistently outperforms MLE under model misspecification, contamination by extreme values, and diverse dependence structures, while maintaining adaptability and computational feasibility.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper introduces a robust estimation framework based solely on the copula function. We begin by introducing a family of divergence measures tailored for copulas, including the (alpha)-, (eta)-, and (gamma)-copula divergences, which quantify the discrepancy between a parametric copula model and an empirical copula derived from data independently of marginal specifications. Using these divergence measures, we propose the minimum copula divergence estimator (MCDE), an estimation method that minimizes the divergence between the model and the empirical copula. The framework proves particularly effective in addressing model misspecifications and analyzing heavy-tailed data, where traditional methods such as the maximum likelihood estimator (MLE) may fail. Theoretical results show that common copula families, including Archimedean and elliptical copulas, satisfy conditions ensuring the boundedness of divergence-based estimators, thereby guaranteeing the robustness of MCDE, especially in the presence of extreme observations. Numerical examples further underscore MCDE's ability to adapt to varying dependence structures, ensuring its utility in real-world scenarios.

Problem

• Robust estimation framework using copula divergence measures
• Addressing model misspecifications and heavy-tailed data analysis
• Ensuring estimator robustness against extreme observations

Innovation

• Copula divergence measures for discrepancy quantification
• Minimum copula divergence estimator for robust estimation
• Boundedness ensuring robustness with extreme observations