Revisiting Randomization with the Cube Method

TL;DR

This paper presents a novel randomization procedure based on the cube method that improves covariate balance and estimation precision in experiments, especially with many covariates, supported by theoretical bounds and simulations.

Contribution

It introduces a new cube method-based randomization procedure that achieves near-exact covariate balance and improves estimation accuracy in experiments.

Findings

Achieves near-exact covariate balance

Provides theoretical bounds on imbalance

Shows improved precision in simulations

Abstract

We introduce a new randomization procedure for experiments based on the cube method, which achieves near-exact covariate balance. This ensures compliance with standard balance tests and allows for balancing on many covariates, enabling more precise estimation of treatment effects using pre-experimental information. We derive theoretical bounds on imbalance as functions of sample size and covariate dimension, and establish consistency and asymptotic normality of the resulting estimators. Simulations show substantial improvements in precision and covariate balance over existing methods, particularly when the number of covariates is large.