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Leveraging the Fisher Randomization Test using Confidence Distributions: Inference, Combination and Fusion Learning

https://doi.org/10.1111/rssb.12429

Luo, Xiaokang ; Dasgupta, Tirthankar ; Xie, Minge ; Liu, Regina Y. ( August 2021 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

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.

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Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution

https://doi.org/10.1080/01621459.2021.1902817

Liu, Dungang ; Liu, Regina Y. ; Xie, Min-ge ( April 2021 , Journal of the American Statistical Association)

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i Fusion: Individualized Fusion Learning

https://doi.org/10.1080/01621459.2019.1672557

Shen, Jieli ; Liu, Regina Y. ; Xie, Min-ge ( January 2020 , Journal of the American Statistical Association)

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Prediction with confidence—A general framework for predictive inference

https://doi.org/10.1016/j.jspi.2017.09.012

Shen, Jieli ; Liu, Regina Y. ; Xie, Min-ge ( May 2018 , Journal of Statistical Planning and Inference)

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