Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 59 min ago
PreprintarXiv licencearXiv

Higher Order Asymptotics of Regression Adjustment Estimators for Causal Inference

  • Anna Kelley
  • Stefan Wager
Open at sourcePDFDOICite

Abstract

Regression adjustment is widely used to improve the precision of average treatment effect estimates from randomized controlled trials. Interacted regression weakly dominates simple regression in terms of its first-order behavior but, in 50-50 randomized trials, the asymptotic variance of both methods is the same and so relative performance is determined by higher-order behavior. Here, we conduct a higher order analysis to compare simple vs. interacted regression adjustments in the equal-probability case. The relative performance of the methods depends on a number of factors including feature skewness, treatment-effect heterogeneity, heteroskedasticity, and nonlinear misspecification, and can favor either estimator. However, in some practically important settings, including when features are skewed and outlying feature values are associated with higher outcome noise, simple regression can outperform interacted regression by a material amount.

Related

  1. Automated, Efficient, and Model-Free Inference for Randomized Clinical Trials via Data-Driven Covariate Adjustment
    Kelly Van Lancker, Ivan Matos Diaz, Stijn Vansteelandt
    The American StatisticianPeer-reviewedLicence not statedFull text15 citedStatisticsOpenAlex
  2. Regression Adjustment for Ratios of Treatment Effects in Randomized Experiments
    Haruo Kakehi
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. Covariate Selection for Doubly Robust Double/debiased Machine Learning Estimators for Causal Inference
    Muwon Kwon, Peter M. Steiner
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  4. Disagreement Among Firm-Level Productivity Estimators and Its Consequences for Applied Inference
    Hongsun Qin, Bin Gao, Wenwen Wang
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref
  5. Finite-population inference for cross-fitted estimators of treatment contrasts in stratified multistage surveys
    M. Ehsan Karim
    arXivPreprintarXiv licenceFull textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{kelley2026higher,
  title = {{Higher Order Asymptotics of Regression Adjustment Estimators for Causal Inference}},
  author = {Anna Kelley and Stefan Wager},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32023},
  eprint = {2610.32023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32023},
}
RIS
TY  - UNPB
TI  - Higher Order Asymptotics of Regression Adjustment Estimators for Causal Inference
AU  - Anna Kelley
AU  - Stefan Wager
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32023
UR  - https://arxiv.org/abs/2610.32023
AB  - Regression adjustment is widely used to improve the precision of average treatment effect estimates from randomized controlled trials. Interacted regression weakly dominates simple regression in terms of its first-order behavior but, in 50-50 randomized trials, the asymptotic variance of both methods is the same and so relative performance is determined by higher-order behavior. Here, we conduct a higher order analysis to compare simple vs. interacted regression adjustments in the equal-probability case. The relative performance of the methods depends on a number of factors including feature skewness, treatment-effect heterogeneity, heteroskedasticity, and nonlinear misspecification, and can favor either estimator. However, in some practically important settings, including when features are skewed and outlying feature values are associated with higher outcome noise, simple regression can outperform interacted regression by a material amount.
ER  -