Consistency of the k-Nearest Neighbor Classifier for Spatially Dependent Data

Abstract

The purpose of this paper is to investigate the k-nearest neighbor classification rule for spatially dependent data. Some spatial mixing conditions are considered, and under such spatial structures, the well known k-nearest neighbor rule is suggested to classify spatial data. We established consistency and strong consistency of the classifier under mild assumptions. Our main results extend the consistency result in the i.i.d. case to the spatial case.

Keywords

Bayes rule / Spatial data / Training data / k-nearest neighbor rule / Mixing condition / Consistency