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

arXiv: https://arxiv.org/abs/2103.03437 · HTML: https://mlsanity.com/paper/2103.03437/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)

## Abstract (arXiv)

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.