Conditional cross-fitting for unbiased machine-learning-assisted covariate adjustment in randomized experiments

TL;DR

This paper introduces a novel conditional cross-fitting method for unbiased covariate adjustment in randomized experiments, addressing finite-sample bias issues and allowing flexible machine learning models under the design-based inference framework.

Contribution

It develops a new conditional cross-fitting approach that ensures unbiased ATE estimation in randomized experiments, even with model misspecification and data reuse.

Findings

Provides unbiased covariate-adjusted ATE estimators.

Develops algorithms for various randomized designs.

Enables valid inference with flexible machine learning models.

Abstract

Randomized experiments are the gold standard for estimating the average treatment effect (ATE). While covariate adjustment can reduce the asymptotic variances of the unbiased Horvitz-Thompson estimators for the ATE, it suffers from finite-sample biases due to data reuse in both prediction and estimation. Traditional sample-splitting and cross-fitting methods can address the problem of data reuse and obtain unbiased estimators. However, they require that the data are independently and identically distributed, which is usually violated under the design-based inference framework for randomized experiments. To address this challenge, we propose a novel conditional cross-fitting method, under the design-based inference framework, where potential outcomes and covariates are fixed and the randomization is the sole source of randomness. We propose sample-splitting algorithms for various randomized experiments, including Bernoulli randomized experiments, completely randomized experiments, and stratified randomized experiments. Based on the proposed algorithms, we construct unbiased covariate-adjusted ATE estimators and propose valid inference procedures. Our methods can accommodate flexible machine-learning-assisted covariate adjustments and allow for model misspecification.