Kaplan-Meier estimators of distance distributions for spatial point processes

• 成果类型: Article
• 署名作者: Baddeley, A; Gill, RD
• 署名单位: University of Western Australia; Utrecht University; Leiden University - Excl LUMC; Leiden University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 263-292
• 关键词: 2nd moment measure; transformations; probability

摘要

When a spatial point process is observed through a bounded window, edge effects hamper the estimation of characteristics such as the empty space function F, the nearest neighbor distance distribution G and the reduced second-order moment function K. Here we propose and study product-limit type estimators of F, G and K based on the analogy with censored survival data: the distance from a fixed point to the nearest point of the process is right-censored by its distance to the boundary of the window. The resulting estimators have a ratio-unbiasedness property that is standard in spatial statistics. We show that the empty space function F of any stationary point process is absolutely continuous, and so is the product-limit estimator of F. The estimators are strongly consistent when there are independent replications or when the sampling window becomes large. We sketch a CLT for independent replications within a fixed observation window and asymptotic theory for independent replications of sparse Poisson processes; In simulations the new estimators are generally more efficient than the border method estimator but (for estimators of K), somewhat less efficient than sophisticated edge corrections.