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On least squares fitting for stationary spatial point processes
Author(s) -
Guan Yongtao,
Sherman Michael
Publication year - 2007
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/j.1467-9868.2007.00575.x
Subject(s) - estimator , asymptotic distribution , consistency (knowledge bases) , mathematics , least squares function approximation , function (biology) , set (abstract data type) , strong consistency , point process , simplicity , point (geometry) , computer science , mathematical optimization , algorithm , statistics , artificial intelligence , philosophy , geometry , epistemology , evolutionary biology , biology , programming language
Summary. The K ‐function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K ‐function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through asymptotic theory, simulation experiments and an application to a data set on long leaf pine‐trees.