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An Affine Invariant kk-Nearest Neighbor Regression Estimate

Abstract

We design a data-dependent metric in Rd\mathbb R^d and use it to define the kk-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard kk-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on kk, and minimal requirements on the input data.

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