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.

翻译：稳健效应量指标（RESI）是近期提出的一种标准化效应量，用于量化不同模型间的关联强度。然而，其置信区间的构建一直依赖于计算密集的自举法。我们利用泰勒展开建立了一个关于RESI渐近分布的通用定理，该定理适用于广泛的模型类别。在线性和逻辑回归等多种设定下的模拟研究表明，与常用的效应量（如Cohen's d和f）相比，RESI及其置信区间具有更小的偏差和更可靠的覆盖率。结合稳健协方差估计，可在模型误设情况下获得有效的推断。我们应用该方法研究了自闭症谱系障碍中抑郁与行为问题同性别及诊断的关联，并证明渐近方法相比自举法可实现高达50倍的加速。我们的工作为自举推断提供了一个可扩展且可靠的替代方案，极大地增强了RESI在高维研究中的适用性。