Parameter estimation for inhomogeneous space-time shot-noise Cox point processes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10328826" target="_blank" >RIV/00216208:11320/16:10328826 - isvavai.cz</a>
Result on the web
<a href="http://onlinelibrary.wiley.com/doi/10.1111/sjos.12222/epdf" target="_blank" >http://onlinelibrary.wiley.com/doi/10.1111/sjos.12222/epdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1111/sjos.12222" target="_blank" >10.1111/sjos.12222</a>

Result language
angličtina
Original language name
Parameter estimation for inhomogeneous space-time shot-noise Cox point processes
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA16-03708S" target="_blank" >GA16-03708S: Spatial geometrical statistics of random sets in Euclidean spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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