Moment estimation for statistics from marked point processes
Dimitris N. Politis, Michael Sherman
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2001 · Volume 63 · Issue 2
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 theirL2-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.
Keywords
Confidence intervals, Large sample inference, Nonparametric estimation, Point processes, Poisson process, Random fields, Subsampling
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