Covariate construction of nonconvex windows for spatial point patterns

Abstract

In some standard applications of spatial point pattern analysis, window selection for spatial point pattern data is complex. Often, the point pattern window is given a priori. Otherwise, the region is chosen using some objective means reflecting a view that the window may be representative of a larger region. The typical approaches used are the smallest rectangular bounding window and convex windows. The chosen window should however cover the true domain of the point process since it defines the domain for point pattern analysis and supports estimation and inference. Choosing too large a window results in spurious estimation and inference in regions of the window where points cannot occur. We propose a new algorithm for selecting the point pattern domain based on spatial covariate information and without the restriction of convexity, allowing for better estimation of the true domain. Amodified kernel smoothed intensity estimate that uses the Euclidean shortest path distance is proposed as validation of the algorithm. The proposed algorithm is applied in the setting of rural villages in Tanzania. As a spatial covariate, remotely sensed elevation data is used. The algorithm is able to detect and filter out high relief areas and steep slopes; observed characteristics that make the occurrence of a household in these regions improbable. Keywords: Covariate, Euclidean shortest path, Nonconvex, Spatial point pattern, Window selection