Leveraging the Fisher Randomization Test using Confidence Distributions: Inference, Combination and Fusion Learning
本文建立了Fisher随机化检验与置信分布的理论联系，从而能明确地反推出置信区间、评估蒙特卡洛样本量对p值曲线的影响，并给出组合多个独立实验检验的方法，适用于有限样本并可直接推广到大样本。
Abstract The flexibility and wide applicability of the Fisher randomization test (FRT) make it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions. Such a connection leads to development’s of (i) an unambiguous procedure for inversion of FRTs to generate confidence intervals with guaranteed coverage, (ii) new insights on the effect of size of the Monte Carlo sample on the estimation of a p-value curve and (iii) generic and specific methods to combine FRTs from multiple independent experiments with theoretical guarantees. Our developments pertain to finite sample settings but have direct extensions to large samples. Simulations and a case example demonstrate the benefit of these new developments.