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 sequential versions of central limit theorem arguments to construct large-sample CSs for causal estimands, with a particular focus on the average treatment effect (ATE) under nonparametric conditions. These CSs allow analysts to update statistical inferences about the ATE in lieu of new data, and experiments can be continuously monitored, stopped, or continued for any data-dependent reason, all while controlling the type-I error rate. Finally, we describe how these CSs readily extend to other causal estimands and estimators, providing a new framework for sequential causal inference in a wide array of problems.
翻译:本文为实验和观察环境的因果关系提供了时间统一信任序列(CS) 。 目标参数 $\ psi$ 的信任序列是一个信任间隔序列 $( t)\\\\\ t=\\\\\\\\\\\\\\\\\\\\infty$, 以便其中每个间隔都同时捕捉$\psi$, 概率高。 这些 CS 提供了任意停留时间对美元/ psi$ 的有效统计推论, 不同于传统的固定时间信任间隔, 需要事先确定样本大小。 现有构建 CSS 的方法侧重于非保护性制度, 其中某些假设( 如已知随机变量的界限) 是一个信任间隔序列 $( $( t)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \