Estimation of the pair correlation function of a spatial point process

Rasmus Waagepetersen, Department of Mathematical Sciences, Aalborg University

The so-called pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. It is of interest in its own right as a summary of the degree of clustering or regularity of a point process. Knowledge of it is further needed e.g. to evaluate standard errors of parameters in a regression model for the intensity function.

Computation of a non-parametric estimate of the pair correlation function is a typical initial step of a statistical analysis of a spatial point pattern. Kernel estimates are popular non-parametric estimates and we will discuss various solutions to the key problem of how to select a suitable kernel band width.

Especially for clustered point patterns, kernel estimates suffer from bias for small spatial lags. We introduce a new orthogonal series estimate which is less biased for clustered point patterns. We consider consistency and asymptotic normality of the new estimate and also finite sample properties in a simulation study. Estimates are finally compared in an application to a data set of tropical rain forest tree locations.