Second‐order quasi‐likelihood for spatial point processes

Applications of spatial point processes for large and complex data sets with inhomogeneities as encountered, example, in tropical rain forest ecology call for estimation methods that are both statistically and computationally efficient. We propose a novel second‐order quasi‐likelihood procedure to estimate the parameters for a second‐order intensity reweighted stationary spatial point process. Our approach is to derive first‐ and second‐order estimating functions and then combine them linearly using appropriate weight functions. In the stationary case, we argue that the asymptotically optimal weight functions are respectively a constant and a function of lags between distinct locations in the observation window. This leads to a considerable gain in computational efficiency. We further exploit this simplification in the nonstationary case. Simulations show that, when compared with several existing approaches, our method can achieve significant gains in statistical efficiency. An application to a tropical rain forest data set further illustrates the advantages of our procedure.