Moment estimation for statistics from marked point processes

Dimitris N. Politis and Michael Sherman

Journal of the Royal Statistical Society Series B, 2001, vol. 63, issue 2, 261-275

Abstract: In spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and we establish their L2‐consistency. The variance estimator in particular can be used for the construction of confidence intervals for estimated parameters. A practical data‐based method for choosing a subsampling parameter is given and illustrated on a data set. Finite sample simulation examples are also presented.

Date: 2001
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