On Nonasymptotic Confidence Intervals for Treatment Effects in Randomized Experiments

TL;DR

This paper develops nonasymptotic confidence intervals for treatment effects in randomized experiments that match the effective sample size of traditional asymptotic intervals, using negative dependence and variance adaptivity.

Contribution

It introduces a method to construct nonasymptotic confidence intervals with optimal effective sample size, closing the gap with asymptotic intervals.

Findings

Nonasymptotic intervals can be as tight as asymptotic ones.

The proposed method achieves optimal rates in an information-theoretic sense.

Performance gap due to propensity score can be eliminated.

Abstract

We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the corresponding central-limit-theorem-based confidence intervals by a factor depending on the square root of the propensity score. We show that this performance gap can be closed, designing nonasymptotic confidence intervals that have the same effective sample size as their asymptotic counterparts. Our approach involves systematic exploitation of negative dependence or variance adaptivity (or both). We also show that the nonasymptotic rates that we achieve are unimprovable in an information-theoretic sense.