Point process learning for non-parametric intensity estimation with focus on Voronoi estimation

Abstract

Point process learning is a new statistical theory that gives us a way to estimate parameters using cross-validation for point processes. By thinning a point pattern we are able to create training and validation sets which are then used in prediction errors. These errors give us a way to measure the discrepancy between two point processes and are used to measure how well the training sets can predict the validation sets. We investigate non-parametric intensity estimation methods with a focus on the resample-smoothing Voronoi estimator. This estimator works by repeatedly thinning a point pattern, finding the Voronoi intensity estimate of the thinned point pattern, and then using the mean as the final intensity estimate. Previously, only a thumb rule was given as to how to choose parameters for the resample-smoothing Voronoi estimator but with the help of point process learning we now have a data-driven method to estimate these parameters.