Asymptotic Distribution of Robust Effect Size Index

2026-01-26

AI Summary

This study addresses the limitations of traditional effect size measures—such as Cohen’s d—which exhibit poor reliability under model misspecification, and overcomes the computational burden of existing confidence intervals for the Robust Effect Size Index (RESI) that rely on computationally expensive bootstrap methods. The authors establish, for the first time, a general asymptotic distribution theory for RESI by leveraging Taylor expansions and robust covariance estimation, yielding an efficient inference framework applicable to a broad class of models including linear and logistic regression. The proposed method achieves up to 50-fold gains in computational speed compared to bootstrap approaches while demonstrating lower bias and more accurate coverage probabilities in both simulation studies and an empirical analysis of autism data, all while maintaining valid inference under model misspecification.

Technology Category

Reasoning under Uncertainty: CausalityIntelligent Robots: State EstimationMachine Learning: Adversarial Learning & Robustness

Application Category

Web Mining and Content Analysis: Robustness and generalizability of Web mining methodsSecurity and Privacy: Large-scale security measurementsSearch and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The Robust Effect Size Index (RESI) is a recently proposed standardized effect size to quantify association strength across models. However, its confidence interval construction has relied on computationally intensive bootstrap procedures. We establish a general theorem for the asymptotic distribution of the RESI using a Taylor expansion that accommodates a broad class of models. Simulations under various linear and logistic regression settings show that RESI and its CI have smaller bias and more reliable coverage than commonly used effect sizes such as Cohen's d and f. Combining with robust covariance estimation yields valid inference under model misspecification. We use the methods to investigate associations of depression and behavioral problems with sex and diagnosis in Autism spectrum disorders, and demonstrate that the asymptotic approach achieves up to a 50-fold speedup over the bootstrap. Our work provides a scalable and reliable alternative to bootstrap inference, greatly enhancing the applicability of RESI to high-dimensional studies.

Problem

• Robust Effect Size Index
• confidence interval
• bootstrap
• asymptotic distribution
• high-dimensional studies

Innovation

• Robust Effect Size Index
• asymptotic distribution
• Taylor expansion
• robust covariance estimation
• bootstrap alternative