A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns
A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns
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DOI：
10.1198/016214507000000879
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发表时间：
2007-12-01
影响因子：
3.7
通讯作者：
Loh, Ji Meng
中科院分区：
文献类型：
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作者：
Guan, Yongtao;Loh, Ji Meng
当模拟非均匀空间点模式时，根据一些测量的协变量来拟合过程的一阶强度函数(FOIF)的参数模型是很有意义的。例如，回归系数的估计可以通过最大化泊松最大似然准则来获得。除了在某些特殊情况下，对其渐近分布的研究很少。在本文中，我们证明了对于一类一般的混合过程，这是渐近正态的。为了估计的方差，我们提出了一种新的稀疏块Bootstrap过程，该过程假设点过程是二阶加权平稳的。要应用这个过程，只需要估计FOIF，而不需要估计过程的任何高阶项。我们建立了由此产生的方差估计的相合性，并通过模拟和对实际数据实例的应用来证明其有效性。
When modeling inhomogeneous spatial point patterns, it is of interest to fit a parametric model for the first-order intensity function (FOIF) of the process in terms of some measured covariates. Estimates for the regression coefficients, say, can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of except in some special cases. In this article we show that is asymptotically normal for a general class of mixing processes. To estimate the variance of, we propose a novel thinned block bootstrap procedure that assumes that the point process is second-order reweighted stationary. To apply this procedure, only the FOIF, and not any high-order terms of the process, needs to be estimated. We establish the consistency of the resulting variance estimator, and demonstrate its efficacy through simulations and an application to a real data example.