Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

Jiří Dvořák; Michaela Prokešová

Applications of Mathematics (2016)

  • Volume: 61, Issue: 4, page 387-411
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Dvořák, Jiří, and Prokešová, Michaela. "Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes." Applications of Mathematics 61.4 (2016): 387-411. <http://eudml.org/doc/283404>.

@article{Dvořák2016,
abstract = {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.},
author = {Dvořák, Jiří, Prokešová, Michaela},
journal = {Applications of Mathematics},
keywords = {space-time point process; shot-noise Cox process; minimum contrast estimation; projection process; increasing domain asymptotics; space-time point process; shot-noise Cox process; minimum contrast estimation; projection process; increasing domain asymptotics},
language = {eng},
number = {4},
pages = {387-411},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes},
url = {http://eudml.org/doc/283404},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Dvořák, Jiří
AU - Prokešová, Michaela
TI - Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 387
EP - 411
AB - 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.
LA - eng
KW - space-time point process; shot-noise Cox process; minimum contrast estimation; projection process; increasing domain asymptotics; space-time point process; shot-noise Cox process; minimum contrast estimation; projection process; increasing domain asymptotics
UR - http://eudml.org/doc/283404
ER -

References

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