Edge-corrected Estimators for the Reduced Second Moment Measure of Point Processes

A new edge-corrected estimator is proposed for the second moment cumulative function K(t) introduced by Ripley (1977, Journal of the Royal Statistical Society, Series B 39, 172–212). This new estimator is compared by simulation methods with existing edge-corrected estimators in the context of both K(t) and L(t) functions which are used to study point patterns. The results of the simulation study suggests that the new estimator provides almost unbiased estimates of K(t) and L(t) and has a smaller mean squared error than its predecessors.