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Title of Journal: Ann Inst Stat Math

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Abbravation: Annals of the Institute of Statistical Mathematics

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Springer Japan

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DOI

10.1016/0014-5793(95)01456-x

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1572-9052

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Twostep estimation procedures for inhomogeneous s

Authors: Michaela Prokešová Jiří Dvořák Eva B Vedel Jensen
Publish Date: 2016/02/27
Volume: 69, Issue: 3, Pages: 513-542
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Abstract

In the present paper we discuss and compare several twostep estimation procedures for inhomogeneous shotnoise Cox processes The intensity function is parametrized by the inhomogeneity parameters while the paircorrelation function is parametrized by the interaction parameters The suggested procedures are based on a combination of Poisson likelihood estimation of the inhomogeneity parameters in the first step and an adaptation of a method from the homogeneous case for estimation of the interaction parameters in the second step The adapted methods based on minimum contrast estimation composite likelihood and Palm likelihood are compared both theoretically and by means of a simulation study The general conclusion from the simulation study is that the three estimation methods have similar performance Twostep estimation with Palm likelihood has not been considered before and is motivated by the superior performance of the Palm likelihood in the stationary case for estimation of certain parameters of interest Asymptotic normality of the twostep estimator with Palm likelihood is provedThis project has been supported by the Czech Science Foundation Project No P201/10/0472 Charles University Grant Agency Project No 664313 and by Centre for Stochastic Geometry and Advanced Bioimaging funded by a Grant from The Villum Foundation We thank the referees for constructive comments and suggestions both concerning the content and exposition of the paper

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