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Non-Parametric Inference Adaptive to Intrinsic Dimension

Khashayar Khosravi, Greg Lewis and Vasilis Syrgkanis

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Abstract: 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.

New Economics Papers: this item is included in nep-ecm
Date: 2019-01, Revised 2019-02
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Handle: RePEc:arx:papers:1901.03719