Premium
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.