The Variance of a New Class of N-point Correlation Estimators in Poisson and Binomial Point Processes

Abstract

We describe a set of new estimators for the N-point correlation functions of point processes. The variance of these estimators is calculated for the Poisson and binomial cases. It is shown that the variance of the unbiased estimator converges to the continuum value much faster than with any previously used alternative, all terms with slower convergence exactly cancel. We compare our estimators with Ripley's $\tK_0$ and $\tK_2$.