Estimation of partially conditional average treatment effect by double kernel-covariate balancing

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