An Affine Invariant $k$-Nearest Neighbor Regression Estimate

Details An Affine Invariant $k$-Nearest Neighbor Regression Estimate An Affine Invariant $k$-Nearest Neighbor Regression Estimate

2012-01-03

arxiv.org/abs/1201.0586v1

Mathematics

Statistics Theory

Scientific paper

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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