Doubly robust confidence sequences for sequential causal inference

This paper derives time-uniform confidence sequences (CS) for causal effects in experimental and observational settings. A confidence sequence for a target parameter $psi$ is a sequence of confidence intervals $(C_t)_{t=1}^infty$ such that every one of these intervals simultaneously captures $psi$ with high probability. Such CSs provide valid statistical inference for $psi$ at arbitrary stopping times, unlike classical fixed-time confidence intervals which require the sample size to be fixed in advance. Existing methods for constructing CSs focus on the nonasymptotic regime where certain assumptions (such as known bounds on the random variables) are imposed, while doubly robust estimators of causal effects rely on (asymptotic) semiparametric theory. We use sequenti