Interval Estimation for Robust Versions of Lorenz Curve IntegratingEmpirical Likelihood Framework With Influence Functions.

Abstract

Real-world data often pose significant challenges for statistical inference due to issues like outliers,
violation of classical assumptions, and inherent heterogeneity. Traditional parametric methods,
heavily reliant on assumptions such as normality and homoscedasticity, frequently yield unreliable
results when applied to skewed distributions, exemplified by income data with extremely high earners.
Empirical likelihood methods have gained prominence to overcome these limitations as they reduce
dependence on strict distributional assumptions. Further robustness is achieved by incorporating
influence functions into empirical likelihood frameworks, explicitly quantifying estimator sensitivity
to data contamination, and improving inference reliability. The Lorenz curve is a crucial economic
measure of income and wealth disparity, but is sensitive to skewness and outliers. This study introduces
robust quantile-based estimators for the Lorenz curve by integrating empirical likelihood and influence
function methodologies. Confidence intervals are constructed through empirical likelihood optimization
using a Lagrange multiplier framework and are evaluated against three bootstrap methods. Extensive
simulations reflecting realistic income distributions demonstrate that the influence function-based
empirical likelihood method significantly outperforms traditional empirical likelihood and other
statistical approaches. Its superior robustness arises primarily from effectively mitigating the distortive
effects of extreme observations. Consequently, this approach ensures reliable inference even under
challenging real-world conditions characterized by data abnormalities. Nevertheless, the proposed
methods present limitations, notably computational complexity and sensitivity to the assumptions
underlying influence functions. Future research should expand its application across socioeconomic
contexts, improve computational efficiency, and deepen theoretical and empirical exploration. This
framework equips researchers and policymakers with precise tools to measure and analyze income inequality.