An affine invariant k-nearest neighbor regression estimate

Authors:
GéRard Biau;Luc Devroye;Vida Dujmović;Adam Krzyak
Affiliations:
LSTA & LPMA, Universitéé Pierre et Marie Curie-Paris VI, Boíte 158, Tour 15-25, 2ème étage, 4 place Jussieu, 75252 Paris Cedex 05, France and DMA, Ecole Normale Supér ...;School of Computer Science, McGill University, Montreal, Canada H3A 2K6;School of Computer Science, Carleton University, 5302 Herzberg Laboratories, 1125 Colonel By Drive, Ottawa, Canada K1S 5B6;Department of Computer Science and Software Engineering, Concordia University, Montreal, Canada H3G 1M8
Venue:
Journal of Multivariate Analysis
Year:
2012

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Abstract

We design a data-dependent metric in 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.