Exploring the Application of Empirical Likelihood Ratios in Robust Non-parametric Statistical Analysis

Posted: Sep 15, 2001

• Hunter Barnes
• Ian Stewart
• Isaac Long

Abstract

The increasing complexity of modern data analysis presents significant challenges for traditional statistical methods, particularly when dealing with heavy-tailed distributions, outliers, and model misspecification. Nonparametric statistics has emerged as a powerful alternative to parametric approaches, offering flexibility and reduced reliance on strict distributional assumptions. However, conventional nonparametric methods often exhibit sensitivity to extreme values and contamination, limiting their practical utility in many real-world applications. This paper addresses these limitations by developing a novel framework that integrates empirical likelihood ratios with robust statistical principles, creating a methodology that combines the flexibility of nonparametric inference with the reliability of robust statistics. Empirical likelihood, introduced by Owen in 1988, provides a nonparametric approach to statistical inference that shares many optimality properties with parametric likelihood methods while requiring minimal assumptions about the underlying data distribution. The empirical likelihood ratio statistic enables the construction of confidence regions and hypothesis tests without specifying the functional form of the data distribution, making it particularly attractive for applications where distributional assumptions are difficult to verify or likely to be violated. Despite these advantages, standard empirical likelihood methods remain vulnerable to the influence of outliers and heavy-tailed distributions, which can severely distort inference and lead to misleading conclusions.