k-nearest neighbors prediction and classification for spatial data

TL;DR

This paper introduces a spatial k-nearest neighbor method that improves nonparametric prediction and classification of spatial data by using a double kernel rule and random bandwidth, with proven convergence properties.

Contribution

It presents a novel spatial k-nearest neighbor approach with a double kernel rule and random bandwidth, along with theoretical convergence results and practical applications.

Findings

Established convergence rates for the predictor

Proved almost sure convergence of classification rule

Demonstrated effectiveness on soil and fisheries datasets

Abstract

This paper proposes a spatial k-nearest neighbor method for nonparametric prediction of real-valued spatial data and supervised classification for categorical spatial data. The proposed method is based on a double nearest neighbor rule which combines two kernels to control the distances between observations and locations. It uses a random bandwidth in order to more appropriately fit the distributions of the covariates. The almost complete convergence with rate of the proposed predictor is established and the almost sure convergence of the supervised classification rule was deduced. Finite sample properties are given for two applications of the k-nearest neighbor prediction and classification rule to the soil and the fisheries datasets