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Improving ratio estimators of second order point process characteristics. (English) Zbl 0963.62089
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.

MSC:
62M30 Inference from spatial processes
62G05 Nonparametric estimation
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