Asymptotic properties of an empirical K-function for inhomogeneous spatial point processes

摘要

The K-function is one of the most commonly used summary statistics. It plays the role for spatial point processes that the covariance function or the variogram plays for continuous observation. The asymptotic properties of the nonparametric estimation of K-function in stationary spatial point processes have been studied. However, in practice, stationary is often not a reasonable assumption. In this article, we investigate the asymptotic behaviour of the nonparametric estimation of K-function for a class of nonstationary processes.