# Article

 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 . Category: math . 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 . Date available: 2016-08-01T09:23:21Z Last updated: 2018-09-03 Stable URL: http://hdl.handle.net/10338.dmlcz/145792 . Reference: [1] Baddeley, A. J., Møller, J., Waagepetersen, R.: Non- and semi-parametric estimation of interaction in inhomogeneous point patterns.Stat. Neerl. 54 (2000), 329-350. 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