Primary Submission Category: Design-Based Causal Inference
Testing individual-level null without imputation
Authors: Zijun Gao,
Presenting Author: Zijun Gao*
An individual-level null specifies restrictions on each unit’s potential outcomes. Fisherian randomization inference provides model-lean, finite-sample–valid tests for a class of such nulls via imputation of potential outcomes. However, for general individual-level nulls, such as a single contrast across multiple treatment levels, the potential outcomes may no longer be imputable. Fisherian randomization inference therefore does not directly apply, and existing approaches typically introduce additional individual-level restrictions and effectively tests a stronger null.
We develop an e-value–based test for general individual-level nulls that circumvents imputation. The key idea is to construct e-values whose validity is directly implied by the restrictions in the null. The proposed test is finite-sample valid, with validity determined solely by the treatment assignment. It also permits data-dependent e-values without sample splitting, yielding adaptive tests with high power. We illustrate the efficacy of our method by testing zero interaction effects in factorial designs.