title: Second-order quasi-likelihood for spatial point processes.
abstract: 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.
authors.affiliation: Program in Applied Mathematics, Yale University, New Haven, Connecticut 06511, U.S.A.
authors.forename: Chong
authors.initials: C
authors.lastname: Deng
authors.affiliation: Department of Management Science, University of Miami, Coral Gables, Florida 33124, U.S.A.
authors.forename: Yongtao
authors.identifier: 0000-0002-9683-9059
authors.initials: Y
authors.lastname: Guan
authors.affiliation: Department of Mathematical Sciences, Aalborg University, Fredrik Bajersvej 7G, Aalborg 9220, Denmark.
authors.forename: Rasmus P
authors.initials: RP
authors.lastname: Waagepetersen
authors.affiliation: Department of Management Science, University of Miami, Coral Gables, Florida 33124, U.S.A.
authors.forename: Jingfei
authors.initials: J
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D001699:Biometry; D003198:Computer Simulation; D004463:Ecology; D015233:Models, Statistical; D065947:Rainforest
keywords: Estimating function; Godambe information; Intensity function; Optimality; Pair correlation function