Gaussian Prepivoting for Finite Population Causal Inference

Abstract

In finite population causal inference exact randomization tests can be constructed for sharp null hypotheses, i.e. hypotheses which fully impute the missing potential outcomes. Oftentimes inference is instead desired for the weak null that the sample average of the treatment effects takes on a particular value while leaving the subject-specific treatment effects unspecified. Without proper care, tests valid for sharp null hypotheses may be anti-conservative should only the weak null hold, creating the risk of misinterpretation when randomization tests are deployed in practice. We develop a general framework for unifying modes of inference for sharp and weak nulls, wherein a single procedure simultaneously delivers exact inference for sharp nulls and asymptotically valid inference for weak nulls. To do this, we employ randomization tests based upon prepivoted test statistics, wherein a test statistic is first transformed by a suitably constructed cumulative distribution function and its randomization distribution assuming the sharp null is then enumerated. For a large class of commonly employed test statistics, we show that prepivoting may be accomplished by employing the push-forward of a sample-based Gaussian measure based upon a suitably constructed covariance estimator. In essence, the approach enumerates the randomization distribution (assuming the sharp null) of a P-value for a large-sample test known to be valid under the weak null, and uses the resulting randomization distribution to perform inference. The versatility of the method is demonstrated through a host of examples, including rerandomized designs and regression-adjusted estimators in completely randomized designs.

References in corpus (4)

• Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique
• Rerandomization to improve covariate balance in experiments
• On regression adjustments in experiments with several treatments
• Beyond the Sharp Null: Randomization Inference, Bounded Null Hypotheses, and Confidence Intervals for Maximum Effects

Cited by in corpus (5)

• Covariate-adjusted Fisher randomization tests for the average treatment effect
• Randomization Inference beyond the Sharp Null: Bounded Null Hypotheses and Quantiles of Individual Treatment Effects
• Rejective Sampling, Rerandomization and Regression Adjustment in Survey Experiments
• Sharp variance estimator and causal bootstrap in stratified randomized experiments
• Prepivoted permutation tests