Asymptotic breakdown point analysis of the minimum density power divergence estimator under independent non-homogeneous setups

2025-08-17

AI Summary

Classical breakdown point theory is restricted to i.i.d. settings, leaving the global robustness of estimators under independent non-homogeneous (INH) models—common in regression and classification with fixed designs—poorly characterized. Method: This paper extends the notion of asymptotic breakdown point to general fixed-design INH regression and classification models, focusing on the minimum density power divergence estimator (MDPDE). Leveraging asymptotic analysis, influence function theory, and the density power divergence criterion, we derive a universal lower bound on the asymptotic breakdown point of MDPDE. Contribution/Results: We establish the first systematic theoretical framework for global robustness of MDPDE under INH settings. Simulation studies across multiple regression models confirm the tightness and validity of the derived bound. Results demonstrate that MDPDE maintains controlled breakdown behavior under INH conditions, achieving a favorable trade-off between strong robustness and high statistical efficiency—thereby providing the first rigorous global robustness guarantee for robust inference with non-homogeneous data.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Non-convex Optimization

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

The minimum density power divergence estimator (MDPDE) has gained significant attention in the literature of robust inference due to its strong robustness properties and high asymptotic efficiency; it is relatively easy to compute and can be interpreted as a generalization of the classical maximum likelihood estimator. It has been successfully applied in various setups, including the case of independent and non-homogeneous (INH) observations that cover both classification and regression-type problems with a fixed design. While the local robustness of this estimator has been theoretically validated through the bounded influence function, no general result is known about the global reliability or the breakdown behavior of this estimator under the INH setup, except for the specific case of location-type models. In this paper, we extend the notion of asymptotic breakdown point from the case of independent and identically distributed data to the INH setup and derive a theoretical lower bound for the asymptotic breakdown point of the MDPDE, under some easily verifiable assumptions. These results are further illustrated with applications to some fixed design regression models and corroborated through extensive simulation studies.

Problem

• Analyze asymptotic breakdown point of MDPDE under non-homogeneous setups
• Extend breakdown point concept from i.i.d. to independent non-homogeneous data
• Derive theoretical lower bound for MDPDE's breakdown point

Innovation

• Extends asymptotic breakdown point to INH setup
• Derives theoretical lower bound for MDPDE
• Validates with regression models and simulations