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Abstract:
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The flexibility and wide applicability of the Fisher randomization test (FRT) makes it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. In spite of a recent surge of interest, certain theoretical and computational aspects of the methodology of inverting FRTs to obtain interval estimators still remain unclear, somewhat limiting its applicability. This research investigates several problems of inversion of FRT to obtain interval estimators, and provides a solution by extending the p-values to a p-value function and then connecting it with confidence distribution (CD). Such a connection is employed to generate interval estimators with statistical guarantees and is also exploited to combine multiple experiments with similar or dissimilar settings. Various algorithms for interval estimators are provided, and corresponding computation problems are discussed. In the end, numerical studies are included to illustrate the performance of our proposed algorithms.
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