We propose a general framework for (multiple) conditional randomization tests that incorporate several important ideas in the recent literature. We establish a general sufficient condition on the construction of multiple conditional randomization tests under which their p-values are independent, in the sense that their joint distribution stochastically dominates the product of uniform distributions under the null. Conceptually, we argue that randomization should be understood as the mode of inference precisely based on randomization. We show that under a change of perspective, many existing statistical methods, including permutation tests for (conditional) independence and conformal prediction, are special cases of the general conditional randomization test. The versatility of our framework is further illustrated with an example concerning lagged treatment effects in stepped-wedge randomized trials. This is joint work with Qingyuan Zhao. The paper draft can be found at https://arxiv.org/abs/2104.10618.
|About the speaker||
Yao Zhang is currently a PhD student at the Department of Applied Mathematics and Theoretical Physics, the University of Cambridge. Prior to this, he studied Mathematics, Statistics and Machine Learning at the University of Cambridge (MA) and the University of Birmingham (BA).