Quasi-likelihood for multivariate spatial point processes with semiparametric intensity functions

We propose a new estimation method to fit a semiparametric intensity function model to multivariate spatial point processes. Our approach is based on the so-called quasi-likelihood that can produce more efficient estimators by accounting for both between- and within-process correlations. To be more specific, we derive the optimal estimating function in a class of first-order estimating functions, where the optimal estimating function depends on the solution to a system of integral equations. We propose a computationally fast approach to obtain an approximate solution to the integral equation, and the resulting estimation approach is therefore computationally efficient. We demonstrate the efficacy of the proposed approach through both simulations and a real application.