Separate versus pooled winsorization for group mean contrasts: a finite-sample theory

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.