Boundary Estimation

Abstract

The existing statistical methods do not provide a satisfactory solution to determining the spatial pattern in spatially referenced data, which is often required by research in many areas including geology, agriculture, forestry, marine science and epidemiology for identifying the source of the unusual environmental factors associated with a certain phenomenon. This work provides a novel algorithm which can be used to delineate the boundary of an area of hot spots accurately and e ciently. Our algorithm, rst of all, does not assume any pre-speci ed geometric shapes for the change-curve. Secondly, the computation complexity by our novel algorithm for changecurve detection is in the order of O(n2), which is much smaller than 2O(n2) required by the CUSP algorithm proposed in M uller&Song [8] and Carlstein's [2] estimators. Furthermore, our novel algorithm yields a consistent estimate of the change-curve as well as the underlying distribution mean of observations in the regions. We also study the hypothesis test of the existence of the change-curve in the presence of independence of the spatially referenced data. We then provide some simulation studies as well as a real case study to compare our algorithm with the popular boundary estimation method : Spatial scan statistic.