An affine invariant k-nearest neighbor regression estimate

Gérard Biau (1) , L. Devroye , L. Dujmovic , A. Krzyzak

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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

Domaines: Probabilités [math.PR]

Gérard Biau, L. Devroye, L. Dujmovic, A. Krzyzak. An affine invariant k-nearest neighbor regression estimate. Journal of Multivariate Analysis, 2012, 112, pp.24-34. ⟨10.1016/j.jmva.2012.05.020⟩. ⟨hal-00717733⟩