Minor Oral: "Conditional Randomization Rank Test"

Abstract: We propose a new method named the Conditional Randomization Rank Test for testing condi- tional independence of a response variable Y and a covariate variable X, conditional on the rest of covari- ates Z. The new method, generalizing the Conditional Randomization Test (CRT) introduced in Cande`s, Fan, Janson and Lv (2018), also relies on the knowledge of the conditional distribution of X|Z and is a conditional sampling based method, easy to implement and interpret. Besides being able to hold exact type 1 error control as well, owing to a more flexible framework, the new method markedly outperforms the CRT in computational efficiency. We establish bounds on the type 1 error in terms of total variation and observed Kullback–Leibler divergence respectively, when the conditional distribution of X|Z is mis- specified. We validate our theoretical results by extensive simulations and show that our new method has considerable advantages over other existing conditional sampling based methods when we take power and efficiency into consideration simultaneously.

Host: Todd Kuffner and Soumendra Lahiri