Affine-invariant depth-based classifiers on the basis of the k-nearest neighbors method

Abstract

Depth-based classifiers on the basis of the k-nearest neighbors method are studied with nonparametric consistency for any continuous distribution. The method of symmetrization of a depth function is proposed, providing a centrally external ordering to determine the nearest neighbors. The construction of a symmetrization asymptotically guarantees the uniqueness of the deepest point that solves the problem of a convex domain with an infinite set of the deepest points. The constructed depth-based classifier based on the depth-based neighborhoods is affine invariant and, therefore, insensitive to extreme values.