Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

In this paper, we exploit a result in point process theory, knowing the expected value of the $K$-function weighted by the true first-order intensity function. This theoretical result can serve as an estimation method for obtaining the parameters estimates of a specific model, assumed for the data. The motivation is to generally avoid dealing with the complex likelihoods of some complex point processes 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, one for each point of the analysed point pattern. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes.