An Affine Invariant $k$-Nearest Neighbor Regression Estimate
Statistics Theory
2012-05-23 v2 Statistics Theory
Abstract
We design a data-dependent metric in and use it to define the -nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard -nearest neighbor regression estimate is asymptotically consistent under the usual conditions on , and minimal requirements on the input data.
Cite
@article{arxiv.1201.0586,
title = {An Affine Invariant $k$-Nearest Neighbor Regression Estimate},
author = {Gérard Biau and Luc Devroye and Vida Dujmovic and Adam Krzyzak},
journal= {arXiv preprint arXiv:1201.0586},
year = {2012}
}