Kaplan-meier Estimators of Interpoint Distance Distributions for Spatial Point Processes

When a spatial point process is observed through a bounded window, edge eeects hamper the estimation of characteristics such as the empty space function F , the nearest neighbour distance distribution G, and the 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 xed 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. The estimators are strongly consistent when there are independent replications or when the sampling window becomes large. In simulations these estimators are generally more eecient than existing estimators. We give some asymptotic theory for large sampling windows and for sparse Poisson processes. Variance estimators are proposed.