A centered Gaussian with smaller covariance assigns at least as much probability as one with larger covariance to any closed convex set with reference probability at least 1/2.
Randomization Tests for Weak Null Hypotheses in Randomized Experiments
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The Fisher randomization test (FRT) is appropriate for any test statistic, under a sharp null hypothesis that can recover all missing potential outcomes. However, it is often sought after to test a weak null hypothesis that the treatment does not affect the units on average. To use the FRT for a weak null hypothesis, we must address two issues. First, we need to impute the missing potential outcomes although the weak null hypothesis cannot determine all of them. Second, we need to choose a proper test statistic. For a general weak null hypothesis, we propose an approach to imputing missing potential outcomes under a compatible sharp null hypothesis. Building on this imputation scheme, we advocate a studentized statistic. The resulting FRT has multiple desirable features. First, it is model-free. Second, it is finite-sample exact under the sharp null hypothesis that we use to impute the potential outcomes. Third, it conservatively controls large-sample type I errors under the weak null hypothesis of interest. Therefore, our FRT is agnostic to the treatment effect heterogeneity. We establish a unified theory for general factorial experiments. We also extend it to stratified and clustered experiments.
years
2026 2representative citing papers
Stochastic sensitivity analysis for matched studies finds worst-case conditional laws for hidden confounders instead of worst-case realizations, controlled by a sensitivity parameter that permits imperfect alignment with potential outcomes and yields higher robustness than conventional methods.
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Gaussian comparison above the median
A centered Gaussian with smaller covariance assigns at least as much probability as one with larger covariance to any closed convex set with reference probability at least 1/2.
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Stochastic Sensitivity Analysis for Matched Observational Studies
Stochastic sensitivity analysis for matched studies finds worst-case conditional laws for hidden confounders instead of worst-case realizations, controlled by a sensitivity parameter that permits imperfect alignment with potential outcomes and yields higher robustness than conventional methods.