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Title: Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes (English)
Author: Dvořák, Jiří
Author: Prokešová, Michaela
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 61
Issue: 4
Year: 2016
Pages: 387-411
Summary lang: English
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Category: math
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Summary: We consider a flexible class of space-time point process models---inhomogeneous shot-noise Cox point processes. They are suitable for modelling clustering phenomena, e.g. in epidemiology, seismology, etc. The particular structure of the model enables the use of projections to the spatial and temporal domain. They are used to formulate a step-wise estimation method to estimate different parts of the model separately. In the first step, the Poisson likelihood approach is used to estimate the inhomogeneity parameters. In the second and third steps, the minimum contrast estimation based on $K$-functions of the projected processes is used to estimate the interaction parameters. We study the asymptotic properties of the resulting estimators and formulate a set of conditions sufficient for establishing consistency and asymptotic normality of the estimators under the increasing domain asymptotics. (English)
Keyword: space-time point process
Keyword: shot-noise Cox process
Keyword: minimum contrast estimation
Keyword: projection process
Keyword: increasing domain asymptotics
MSC: 60G55
MSC: 62F12
idZBL: Zbl 06644003
idMR: MR3532250
DOI: 10.1007/s10492-016-0138-6
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Date available: 2016-08-01T09:23:21Z
Last updated: 2018-09-03
Stable URL: http://hdl.handle.net/10338.dmlcz/145792
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