An Affine Invariant K-Nearest Neighbor Regression Estimate

We design a data-dependent metric in lie and use it to define the k-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on k, and minimal requirements on the input data. (C) 2012 Elsevier Inc. All rights reserved.