Asymptotic Distribution of Robust Effect Size Index

Thomas M. Menino Convention & Exhibition Center 

The Robust Effect Size Index (RESI) is a recently proposed standardized index to quantify effect magnitude across models, with growing applications in high-dimensional settings such as neuroimaging. Existing confidence interval (CI) construction relies on computationally intensive bootstrap methods. We establish a general theorem for the asymptotic distribution of RESI using a Taylor expansion, applicable to a broad class of models. Simulations under linear and logistic 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. When combined with robust covariance estimation, our method provides valid inference under model misspecification, a critical aspect in neuroimaging where spatial dependence and heterogeneous variances across regions are common. Moreover, our approach substantially reduces computation time, achieving up to a 50-fold speedup compared to bootstrap procedures. Building on our earlier work on confidence sets for imaging studies, this paper offers a scalable and reliable alternative for RESI inference, significantly enhancing its applicability to neuroimaging and other complex data type

Semiparametric

Generalized linear model

Hypothesis testing 

IMS