Strong consistency of a kernel-based rule for spatially dependent data

Abstract

We consider the kernel-based classifier proposed by Younso (2017). This nonparametric classifier allows for the classification of missing spatially dependent data. The weak consistency of the classifier has been studied by Younso (2017). The purpose of this paper is to establish strong consistency of this classifier under mild conditions. The classifier is discussed in a multi-class case. The results are illustrated with simulation studies and real applications.

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

“…This model is mostly used to classify data produced by social network analysis taking into account the connection between nodes, but without any influence of the spatial coordinates. [18,17,19,20,21] deal with kernel-based rules to classify temporally and spatially dependent data, and study asymptotic properties of classifiers. The aim of the present paper is to investigate whether the classical k-nearest neighbor classifier can be extended to classify spatial data.…”

“…The main difficulties with the kernel method appear when data are sparse; choosing the number of neighbors allows to avoid this problem and is adapted to the concentration of the data. Consistency of kernel-based rules on temporally or spatially dependent data has recently been investigated by [18,17,19,20,21] in finite and infinite-dimensional space. In this paper, we will establish the (strong) consistency of the k-nearest neighbor classifier for spatially dependent data.…”