Doubly robust confidence sequences for sequential causal inference

03/11/2021
by   Ian Waudby-Smith, et al.
0

This paper derives time-uniform confidence sequences (CS) for causal effects in experimental and observational settings. A confidence sequence for a target parameter ψ is a sequence of confidence intervals (C_t)_t=1^∞ such that every one of these intervals simultaneously captures ψ with high probability. Such CSs provide valid statistical inference for ψ 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/25/2022

Semiparametric Estimation on Multi-treatment Causal Effects via Cross-Fitting

Causal inference is a critical research area with multi-disciplinary ori...
research
10/18/2018

Uniform, nonparametric, non-asymptotic confidence sequences

A confidence sequence is a sequence of confidence intervals that is unif...
research
08/17/2022

Debiased Inference on Identified Linear Functionals of Underidentified Nuisances via Penalized Minimax Estimation

We study generic inference on identified linear functionals of nonunique...
research
10/18/2022

Heteroscedasticity-aware sample trimming for causal inference

A popular method for variance reduction in observational causal inferenc...
research
02/17/2022

Locally private nonparametric confidence intervals and sequences

This work derives methods for performing nonparametric, nonasymptotic st...
research
10/17/2022

A Design-Based Riesz Representation Framework for Randomized Experiments

We describe a new design-based framework for drawing causal inference in...
research
03/08/2023

Inference on Optimal Dynamic Policies via Softmax Approximation

Estimating optimal dynamic policies from offline data is a fundamental p...

Please sign up or login with your details

Forgot password? Click here to reset