A1284
Title: Regression adjustment with high-dimensional covariates
Authors: Dogyoon Song - University of California Davis (United States) [presenting]
Abstract: Regression adjustment is a classical technique in causal inference that leverages covariates to improve precision in randomized controlled trials (RCTs) or to adjust for confounding in observational studies. While well-understood in low-dimensional settings, its behavior in modern high-dimensional regimes---where the number of covariates may exceed the number of observations---remains less explored. In particular, existing theoretical results are largely asymptotic, rely on residual-based analysis, and provide limited insights about finite-sample inference when $p > n$. Regression adjustment in high-dimensional RCT settings is revisited. We present a non-asymptotic analysis of the regression-adjusted average treatment effect estimator, by leveraging tools from concentration of measure to quantify uncertainty without relying on classical asymptotic variance estimation, and further controlling finite-sample bias via Steins method. Thereafter, we conclude by discussing potential extensions of these techniques to causal inference problems involving random objects beyond real-valued responses.
