Moment estimation for statistics from marked point processes | Zendy

Politis Dimitris N. | Zendy; Sherman Michael | Zendy

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Moment estimation for statistics from marked point processes

Author(s) -

Politis Dimitris N.,

Sherman Michael

Publication year - 2001

Publication title -

journal of the royal statistical society: series b (statistical methodology)

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 6.523

H-Index - 137

eISSN - 1467-9868

pISSN - 1369-7412

DOI - 10.1111/1467-9868.00284

Subject(s) - estimator , point process , consistency (knowledge bases) , statistics , moment (physics) , mathematics , point estimation , realization (probability) , variance (accounting) , data set , point (geometry) , confidence interval , set (abstract data type) , data point , sample (material) , computer science , physics , geometry , accounting , chemistry , classical mechanics , chromatography , business , programming language

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 L 2 ‐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.

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