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Parameter Estimation for Inhomogeneous Space‐Time Shot‐Noise Cox Point Processes
Author(s) -
Dvořák Jiří,
Prokešová Michaela
Publication year - 2016
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12222
Subject(s) - projection (relational algebra) , mathematics , point process , consistency (knowledge bases) , projection method , cox process , noise (video) , moment (physics) , estimator , shot noise , curse of dimensionality , process (computing) , algorithm , computer science , artificial intelligence , statistics , dykstra's projection algorithm , geometry , poisson distribution , image (mathematics) , telecommunications , physics , classical mechanics , detector , poisson process , operating system
We consider the problem of parameter estimation for inhomogeneous space‐time shot‐noise Cox point processes. We explore the possibility of using a stepwise estimation method and dimensionality‐reducing techniques to estimate different parts of the model separately. We discuss the estimation method using projection processes and propose a refined method that avoids projection to the temporal domain. This remedies the main flaw of the method using projection processes – possible overlapping in the projection process of clusters, which are clearly separated in the original space‐time process. This issue is more prominent in the temporal projection process where the amount of information lost by projection is higher than in the spatial projection process. For the refined method, we derive consistency and asymptotic normality results under the increasing domain asymptotics and appropriate moment and mixing assumptions. We also present a simulation study that suggests that cluster overlapping is successfully overcome by the refined method.