{"ID":2843563,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.08539","arxiv_id":"2511.08539","title":"Neumann-series corrections for regression adjustment in randomized experiments","abstract":"We study average treatment effect (ATE) estimation under complete randomization with many covariates in a design-based, finite-population framework. In randomized experiments, regression adjustment can improve precision of estimators using covariates, without requiring a correctly specified outcome model. However, existing design-based analyses establish asymptotic normality only up to $p = o(n^{1/2})$, extendable to $p = o(n^{2/3})$ with a single de-biasing. We introduce a novel theoretical perspective on the asymptotic properties of regression adjustment through a Neumann-series decomposition, yielding a systematic higher-degree corrections and a refined analysis of regression adjustment. Specifically, for ordinary least squares regression adjustment, the Neumann expansion sharpens analysis of the remainder term, relative to the residual difference-in-means. Under mild leverage regularity, we show that the degree-$d$ Neumann-corrected estimator is asymptotically normal whenever $p^{ d+3}(\\log p)^{ d+1}=o(n^{ d+2})$, strictly enlarging the admissible growth of $p$. The analysis is purely randomization-based and does not impose any parametric outcome models or super-population assumptions.","short_abstract":"We study average treatment effect (ATE) estimation under complete randomization with many covariates in a design-based, finite-population framework. In randomized experiments, regression adjustment can improve precision of estimators using covariates, without requiring a correctly specified outcome model. However, exis...","url_abs":"https://arxiv.org/abs/2511.08539","url_pdf":"https://arxiv.org/pdf/2511.08539v1","authors":"[\"Dogyoon Song\"]","published":"2025-11-11T18:17:54Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}