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Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes
Author(s) -
Davies Tilman M.,
Hazelton Martin L.
Publication year - 2013
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12011
Subject(s) - contrast (vision) , cox process , mathematics , univariate , point process , parametric statistics , gaussian process , gaussian , offset (computer science) , flexibility (engineering) , computer science , algorithm , statistics , mathematical optimization , multivariate statistics , artificial intelligence , physics , quantum mechanics , programming language , poisson distribution , poisson process
The univariate log‐Gaussian Cox process (LGCP) has shown considerable potential for the flexible modelling of the spatial, and more recently, spatiotemporal, intensity functions of planar point patterns within a restricted region in space. Its flexibility and mathematical tractability are partly offset by the need to acquire sensible estimates of the parameters controlling the dependence structure of the Gaussian field given the observed data. The method of minimum contrast, which compares theoretical descriptors of the process with their non‐parametric counterparts in order to obtain the required estimates, is arguably the most popular in practice to date. This article provides a comprehensive set of simulation studies focused on gauging the performance and impact of minimum contrast methods for parameter estimation of these processes. Results indicate that concerns over arbitrariness of implementation of minimum contrast give way to satisfactory practical performance.