On Nonparametric Variance Estimation for Second-Order Statistics of Inhomogeneous Spatial Point Processes With a Known Parametric Intensity Form

• 成果类型: Article
• 署名作者: Guan, Yongtao
• 署名单位: Yale University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08541
• 发表日期: 2009
• 页码: 1482-1491
• 关键词: residual analysis

摘要

We introduce new variance estimation procedures for second-order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes. The statistics are defined either on a subset B of the observation window or on the whole window. For the former, we use subblocks that have the same size and shape as B as replicates of B in order to estimate the target variance. For the latter, we develop a subsampling estimator for a key component in the target variance and estimate its other components by method-of-moment methods. Under some suitable conditions, we prove that the proposed variance estimators are consistent for the target variances in both cases. Simulations and an application to a real data example are used to demonstrate the usefulness of the proposed methods. This article has supplementary material online.