Weights-based inference for the cross-fitted averaged MCF estimator

Develop a valid weights-based inference procedure for the cross-fitted averaged Modified Causal Forest estimator (mcf-cent-eff), which averages two two-sample honesty-based MCF fits for individualized average treatment effects and yields correlated components. The procedure should correctly account for the correlation between the averaged components and provide asymptotically valid standard errors and confidence intervals.

Background

The Modified Causal Forest (MCF) uses a two-sample honesty scheme to estimate individualized average treatment effects (IATEs) and supports a weights-based variance estimator for inference. To improve efficiency when inference is not the primary goal, the authors propose a cross-fitted variant (mcf-cent-eff) that averages two estimates obtained by swapping the roles of the two honest subsamples. However, this averaging introduces correlation between the components, and the current weights-based inference routine does not address this dependency.

The authors note a practical workaround—using conservative normal-based inference with the variance taken as the average of the single-estimation variances—but they highlight that a rigorous, dedicated inference method for the averaged estimator is lacking.