Deng Chong, Guan Yongtao, Waagepetersen Rasmus P, Zhang Jingfei
Program in Applied Mathematics, Yale University, New Haven, Connecticut 06511, U.S.A.
Department of Management Science, University of Miami, Coral Gables, Florida 33124, U.S.A.
Biometrics. 2017 Dec;73(4):1311-1320. doi: 10.1111/biom.12694. Epub 2017 Mar 29.
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.
对于在热带雨林生态学等领域中遇到的具有不均匀性的大型复杂数据集，空间点过程的应用需要既具有统计效率又具有计算效率的估计方法。我们提出了一种新颖的二阶拟似然程序，用于估计二阶强度加权平稳空间点过程的参数。我们的方法是推导一阶和二阶估计函数，然后使用适当的权重函数将它们线性组合。在平稳情况下，我们认为渐近最优权重函数分别是一个常数和观测窗口中不同位置之间滞后的函数。这导致计算效率有相当大的提高。我们在非平稳情况下进一步利用这种简化。模拟表明，与几种现有方法相比，我们的方法在统计效率方面可以实现显著提高。对热带雨林数据集的应用进一步说明了我们程序的优点。
