Lasso adjustments of treatment effect estimates in randomized experiments

Area of Science:

• Statistics
• Econometrics
• Biostatistics
• Machine Learning

Background:

• Analyzing randomized experiments often involves adjusting for covariates using multivariate regression to reduce variance.
• High-dimensional covariates (more covariates than observations) can lead to overfitting and poor performance with standard regression.
• The Least Absolute Shrinkage and Selection Operator (Lasso) offers a potential solution for high-dimensional data analysis.

Purpose of the Study:

• To develop and evaluate a principled method for analyzing randomized experiments with a large number of covariates.
• To assess the efficiency of a Lasso-based treatment effect estimator compared to the difference-of-means estimator.
• To provide a method for constructing tighter confidence intervals in such settings.

Main Methods:

• The study investigates a treatment effect estimator derived from applying Lasso within the Neyman-Rubin model of randomized experiments.
• Theoretical conditions are derived to demonstrate the estimator's efficiency gains over the simple difference-of-means.
• A conservative estimator for asymptotic variance is proposed, facilitating improved confidence interval construction.

Main Results:

• The Lasso-based estimator is theoretically guaranteed to be more efficient than the difference-of-means estimator under specific conditions.
• A conservative estimator of asymptotic variance allows for tighter confidence intervals.
• Simulations and data examples indicate that Lasso adjustment is beneficial even when the number of covariates is less than the number of observations.

Conclusions:

• Lasso-based adjustment provides a statistically sound and efficient method for analyzing randomized experiments, particularly when dealing with numerous covariates.
• A hybrid approach combining Lasso for variable selection and Ordinary Least Squares (OLS) for estimation demonstrates strong performance.
• The proposed methods offer advantages in variance reduction and confidence interval precision over traditional difference-of-means approaches.