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Primary Submission Category: Evidence Factors and Causal Inference

Statistical and Causal Robustness for Causal Null Hypothesis Tests

Authors: Rohit Bhattacharya, Junhui Yang, Ted Westling,

Presenting Author: Rohit Bhattacharya*

Applications of semiparametric theory to causal inference typically focus on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Often, an analyst might consider multiple plausible causal models given a single observed dataset. Evidence factors have recently been proposed as an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. In this talk, we present a method that combines semiparametric theory with evidence factors. We propose a causal null hypothesis test based on joint asymptotic normality of $k$ asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of $k$ candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the $k$ proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance parameters. We conclude by discussing relative advantages and disadvantages of the proposed method.