On the effect of intensity estimation on K-function estimate for spatial Poisson point patterns

This thesis investigates the optimization of intensity estimation methods of the K-function estimate for spatial point pattern analysis, which is a second-order summary statistic highlighting the type of interaction among points in terms of clustering, regularities, and randomness. To accomplish this, a simulation study was conducted to assess the impact of various intensity estimators, intensity rescaling factors, and edge corrections on non-parametric estimators of K-functions. The study considers homogeneous and inhomogeneous Poisson point patterns, employing Kernel-based and Voronoi-based intensity estimators. The obtained results (based on bias, variance, and MSE) demonstrate that the non-parametric estimators of K-functions yield a more accurate identification of a homogeneous point pattern when a kernel-based intensity is used, whereas, when met with an inhomogeneous point pattern, the non-parametric estimators of K-functions identifies the type of interaction among points better when a Voronoi-based intensity estimator is utilized. These findings contribute valuable insights and evidence-based recommendations for improving the influence of intensity estimation on K-functions for spatial Poisson point patterns.