An Affine Invariant k-Nearest Neighbor Regression Estimate

2012/01/03 by Gérard Biau, Luc Devroye, Biau, Gérard +7
Mathematics · #Advanced Statistical Methods and Models #Point processes and geometric inequalities #Statistical Methods and Inference #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1201.0586

arxiv created 2012/05/18 · arxiv updated 2012/05/23

Abstract

We design a data-dependent metric in \mathbb R^d 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.

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