A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns

• 成果类型: Article
• 署名作者: Guan, Yongtao; Loh, Ji Meng
• 署名单位: Yale University; Columbia University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214507000000879
• 发表日期: 2007
• 页码: 1377-1386
• 关键词: STATISTICS; isotropy

摘要

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.