Minimum contrast for estimating point processes intensity

Abstract

A result in point process theory, based on the expectation of the weighted K-function, is exploited by the true first-order intensity function. This theoretical result can be an estimation method for obtaining the parameter estimates of a specific model assumed for the data. The motivation is to avoid dealing with the complex likelihoods of some complex point process models and their maximization. This can be more evident when considering the local second-order characteristics since the proposed method can estimate the vector of the local parameters corresponding to the points of the analysed point pattern. We illustrate the method through simulation studies for purely spatial and spatio-temporal point processes.