Improving ratio estimators of second order point process characteristics (Q2711681)

The Ripley \(K(r)\) function of a stationary point process (reduced second moment function) is the mean number of \(r\)-close pairs of points per unit volume divided by the intensity of the process (\(\lambda\)). Usual estimators for \(K(r)\) use a ratio of estimators for \(\lambda^2 K(r)\) and \(\lambda^2\). The authors consider some of such estimators and demonstrate how to use them in such a way that the bias of the numerator compensates the bias of the denominator. Estimators of the \(L\)-function and the pair correlation function (a normalized derivative of the \(K\)-function) are also considered. Results of simulations are presented.