Leveraging the Fisher randomization test using confidence distributions: Inference, combination and fusion learning

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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.

Original languageEnglish (US)
Pages (from-to)777-797
Number of pages21
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume83
Issue number4
DOIs
StatePublished - Sep 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • exact test
  • fiducial
  • model-free
  • monte carlo
  • p-value
  • sharp nulle

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