B1000
Title: Statistical testing under distributional shifts: Applications in causal inference
Authors: Niklas Pfister - University of Copenhagen (Denmark) [presenting]
Abstract: Statistical hypothesis testing is a central problem in empirical inference. Observing data from a distribution $P$, one is interested in testing whether $P$ lies in a given null hypothesis while controlling the probability of false rejections. We will introduce a framework for statistical testing under distributional shifts. The goal will be to test a target hypothesis $P$ in $H_0$ using observed data from a distribution $Q$, where we assume that $P$ is related to $Q$ through a known distributional shift. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set (mimicking properties of $P$) and then applies an existing test in the target domain. We prove that this procedure holds pointwise asymptotic level if the target test holds pointwise asymptotic level, the size of the resample is at most of order $\sqrt{n}$, and the resampling weights are well-behaved. We will see that testing under distributional shifts naturally arises in causal inference and that the proposed procedure provides an easy-to-use and general-purpose solution to a wide variety of causal inference tasks.