Before revision:  We show that if the intrinsic dimension of the co-variate distribution is equal to d, then the finite sample estimation error of our estimator is of order n^{-1/(d+2)} and our estimate is n^{1/(d+2)}-asymptotically normal, irrespective of D  . We discuss extensions and applications to heterogeneous treatment effect estimation.
After revision:  We show that if the intrinsic dimension of the co-variate distribution is equal to d, then the finite sample estimation error of our estimator is of order n^{-1/(d+2)} and our estimate is n^{1/(d+2)}-asymptotically normal, irrespective of D . The sub-sampling size required for achieving these results depends on the unknown intrinsic dimension d. We propose an adaptive data-driven approach for choosing this parameter and prove that it achieves the desired rates . We discuss extensions and applications to heterogeneous treatment effect estimation.