Design-based finite-sample analysis for regression adjustment

TL;DR

This paper develops a finite-sample, design-based framework for regression adjustment in randomized experiments, providing valid confidence intervals even in high-dimensional settings where covariates outnumber observations.

Contribution

It introduces a non-asymptotic analysis that yields explicit, instance-adaptive confidence intervals for the regression-adjusted ATE estimator in high-dimensional regimes.

Findings

Finite-sample confidence intervals are valid even when p > n.

Covariate geometry influences the concentration and bias of the estimator.

The approach uses variance-adaptive martingales and Stein's method for analysis.

Abstract

In randomized experiments, regression adjustment can improve the precision of average treatment effect (ATE) estimation using covariates without requiring a correctly specified outcome model. Although well studied in low-dimensional settings, its behavior in high-dimensional regimes, where the number of covariates $p$ may exceed the number of observations $n$, remains underexplored. Moreover, existing analyses are largely asymptotic, providing limited guidance for finite-sample inference. We develop a design-based, non-asymptotic framework for analyzing the regression-adjusted ATE estimator under complete randomization. This yields finite-sample-valid confidence intervals with explicit, instance-adaptive widths, even when $p > n$. While these intervals rely on oracle (population-level) quantities, we also outline data-driven envelopes computable from observed data. Our approach hinges on a refined swap sensitivity analysis of an estimator: stochastic fluctuation is controlled via a variance-adaptive Doob martingale and Freedman's inequality, and design bias is bounded by Stein's method of exchangeable pairs. The analysis elucidates how covariate geometry governs concentration and bias of the adjusted estimator, suggesting when and how regression adjustment can be effective.