Problem
Research questions and friction points this paper is trying to address.
winsorization
group mean contrasts
heavy-tailed outcomes
finite-sample theory
pooled versus separate
Separate versus pooled winsorization for group mean contrasts: a finite-sample theory
🤖 AI Summary
This study addresses the sensitivity of group mean comparison estimators to outliers under heavy-tailed data, where conventional Winsorization lacks theoretical justification. The authors systematically compare the finite-sample properties of group-wise independent Winsorization and pooled Winsorization, establishing for the first time that the pooled approach fails to achieve sub-Gaussian convergence rates. In contrast, group-wise independent Winsorization not only attains this optimal rate but also extends naturally to general linear mean contrasts. Through finite-sample bias bounds, sub-Gaussian concentration inequalities, and numerical simulations, the proposed method is shown to be nearly unbiased and exhibit superior concentration, substantially outperforming the pooled strategy. These results provide rigorous theoretical support and practical guidance for robust mean comparison in real-world applications.
📝 Abstract
Comparing group means is foundational to many statistical areas, including two-sample studies, randomized trials, and difference-in-differences designs, yet heavy-tailed outcomes can make conventional estimators unstable. A common remedy is to winsorize the data before estimating the target mean contrast. The dominant approach, pooled winsorization, computes winsorization thresholds from the combined sample across all groups, while the rarely used alternative, separate winsorization, computes them within each group. We study finite-sample deviation bounds for these two winsorization strategies, and we prove an impossibility result: no deterministic rule for selecting the pooled winsorization level can attain the sub-Gaussian rate. In contrast, separate winsorization attains this rate, and the guarantee extends to general linear contrasts of group means. Simulation studies confirm that pooled winsorization can have substantial bias, while separate winsorization remains nearly unbiased and concentrates well around the truth. These results support a simple recommendation: winsorize within each group rather than after pooling.
Innovation
Methods, ideas, or system contributions that make the work stand out.
winsorization
finite-sample theory
sub-Gaussian rate
group mean contrast
heavy-tailed data
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