Targeted smoothing parameter selection for estimating average causal effects

TL;DR

This paper introduces data-driven methods for selecting smoothing parameters in non-parametric causal effect estimation, improving accuracy over existing techniques like cross-validation.

Contribution

It proposes a novel approach to choose smoothing parameters specifically for average causal effect estimation by estimating the mean squared error directly.

Findings

Proposed methods outperform cross-validation in simulations.

Smoothing parameters converge faster to zero for causal effect estimation.

Lower empirical mean squared error achieved with the new methods.

Abstract

The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which regulates the amount of degrees of freedom used in the fit. In this paper we propose data-driven methods for selecting smoothing parameters when the targeted parameter is an average causal effect. For this purpose, we propose to estimate the exact expression of the mean squared error of the estimators. Asymptotic approximations indicate that the smoothing parameters minimizing this mean squared error converges to zero faster than the optimal smoothing parameter for the estimation of the regression functions. In a simulation study we show that the proposed data-driven methods for selecting the smoothing parameters yield lower empirical mean squared error than other methods available such as, e.g., cross-validation.