Randomisation inference beyond the sharp null: bounded null hypotheses and quantiles of individual treatment effects
本文重新解释随机化检验，证明其可检验个体效应均非正（或均非负）的有界零假设，并推广到个体效应分位数的精确推断，无需多重比较校正。
Abstract Randomisation inference (RI) is typically interpreted as testing Fisher’s ‘sharp’ null hypothesis that all unit-level effects are exactly zero. This hypothesis is often criticised as restrictive and implausible, making its rejection scientifically uninteresting. We show, however, that many randomisation tests are also valid for a ‘bounded’ null hypothesis under which the unit-level effects are all non-positive (or all non-negative) but are otherwise heterogeneous. In addition to being more plausible a priori, bounded nulls are closely related to substantively important concepts such as monotonicity and Pareto efficiency. Reinterpreting RI in this way expands the range of inferences possible in this framework. We show that exact confidence intervals for the maximum (or minimum) unit-level effect can be obtained by inverting tests for a sequence of bounded nulls. We also generalise RI to cover inference for quantiles of the individual effect distribution as well as for the proportion of individual effects larger (or smaller) than a given threshold. The proposed confidence intervals for all effect quantiles are simultaneously valid, in the sense that no correction for multiple analyses is required. In sum, our reinterpretation and generalisation provide a broader justification for randomisation tests and a basis for exact non-parametric inference for effect quantiles.