The Role of Empirical Likelihood Estimation in Improving Robustness in Modern Statistical Inference

Posted: Mar 20, 2021

• Mason Davis
• Mason Allen
• Grace Nelson

Abstract

The landscape of modern statistical inference faces unprecedented challenges as data complexity increases and traditional parametric assumptions frequently fail to hold in practice. Conventional statistical methods, particularly those based on maximum likelihood estimation, demonstrate remarkable efficiency when underlying model assumptions are satisfied but exhibit significant vulnerability to various forms of model misspecification, data contamination, and distributional anomalies. This fragility has profound implications across scientific domains, from financial risk assessment to environmental modeling, where erroneous inferences can lead to substantial real-world consequences. The empirical likelihood framework, introduced by Owen in the late 1980s, offers a nonparametric alternative that constructs likelihood ratios without requiring explicit distributional assumptions. However, traditional empirical likelihood methods have limitations in high-dimensional settings and often suffer from efficiency losses compared to their parametric counterparts when model assumptions are correct. This research addresses these challenges by developing a novel hybrid methodology that integrates the robustness properties of empirical likelihood with the adaptive capacity of modern machine learning techniques. Our approach represents a paradigm shift in robust statistical inference by creating a framework that dynamically adjusts its behavior based on evidence from the data, effectively balancing the trade-off between robustness and efficiency without requiring explicit specification of contamination mechanisms. The core innovation lies in our integration of neural density estimators with empirical likelihood constraints, enabling the method to learn complex data structures while maintaining desirable statistical properties.