  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.
