Estimation of Partially Conditional Average Treatment Effect by Hybrid Kernel-covariate Balancing

TL;DR

This paper introduces a novel hybrid kernel weighting estimator for nonparametric estimation of the partially conditional average treatment effect, effectively controlling confounder balancing without strict smoothness assumptions.

Contribution

It proposes a new kernel-based estimator with an augmented version that incorporates outcome mean functions, along with gradient algorithms for optimization and asymptotic analysis under relaxed assumptions.

Findings

Estimator performs well in simulations

Application to smoking and birth weight demonstrates practical utility

Relaxed assumptions improve robustness of treatment effect estimation

Abstract

We study nonparametric estimation for the partially conditional average treatment effect, defined as the treatment effect function over an interested subset of confounders. We propose a hybrid kernel weighting estimator where the weights aim to control the balancing error of any function of the confounders from a reproducing kernel Hilbert space after kernel smoothing over the subset of interested variables. In addition, we present an augmented version of our estimator which can incorporate estimations of outcome mean functions. Based on the representer theorem, gradient-based algorithms can be applied for solving the corresponding infinite-dimensional optimization problem. Asymptotic properties are studied without any smoothness assumptions for propensity score function or the need of data splitting, relaxing certain existing stringent assumptions. The numerical performance of the proposed estimator is demonstrated by a simulation study and an application to the effect of a mother's smoking on a baby's birth weight conditioned on the mother's age.