Non-Parametric Inference Adaptive to Intrinsic Dimension

01/11/2019

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by   Khashayar Khosravi, et al.

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We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension D of the conditioning variable is larger than the sample size n, estimation and inference is feasible as long as the distribution of the conditioning variable has small intrinsic dimension d, as measured by the doubling dimension. Our estimation is based on a sub-sampled ensemble of the k-nearest neighbors Z-estimator. 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.