High-dimensional regression adjustments in randomized experiments

2016/07/22 by Stefan Wager, Wenfei Du, Jonathan Taylor +1 · 1 voice · 1 citation
Mathematics · #Advanced Causal Inference Techniques #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #stat.ME #stat.ML

paper · pdf · doi:10.1073/pnas.1614732113

To appear in the Proceedings of the National Academy of Sciences. The present draft does not reflect final copyediting by the PNAS staff

arxiv published 2016/07/22 · openalex publication_date 2016/10/25 · arxiv created 2016/10/27 · arxiv updated 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information, and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the average treatment effect. Our results considerably extend the range of settings where high-dimensional regression adjustments are guaranteed to provide valid inference about the population average treatment effect. We then propose cross-estimation, a simple method for obtaining finite-sample-unbiased treatment effect estimates that leverages high-dimensional regression adjustments. Our method can be used when the regression model is estimated using the lasso, the elastic net, subset selection, etc. Finally, we extend our analysis to allow for adaptive specification search via cross-validation, and flexible non-parametric regression adjustments with machine learning methods such as random forests or neural networks.

Citations

• On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9
• Atomic Decomposition by Basis Pursuit
• Estimating causal effects of treatments in randomized and nonrandomized studies.
• On regression adjustments to experimental data
• Decomposing Treatment Effect Variation
• Confidence Intervals for High-Dimensional Linear Regression: Minimax Rates and Adaptivity
• Recent Developments in the Econometrics of Program Evaluation
• The Econometrics of Randomized Experiments
• Estimation and Inference of Heterogeneous Treatment Effects using Random Forests
• High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification

Cited by

• Regression adjustment in completely randomized experiments with a diverging number of covariates

Discussions

• Haha fair, but you could turn that into regression_forest(X,y), which can learn interactions and polynomials (as long as you cross-fit). high-dim regression version: arxiv.org/abs/1607.06801 general M [bsky, 2 points, 0 comments]

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