Asymptotic Palm likelihood theory for stationary point processes

Prokešová, Michaela; Jensen, Eva B. Vedel

doi:10.1007/s10463-012-0376-7

Cited by 26 publications

(39 citation statements)

References 27 publications

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“…Palm likelihood inference for M 1 and M 2 was considered in Tanaka et al (2007), where the two models are called the Thomas model and generalized Thomas model of type B, respectively. Prokešová and Jensen (2010) showed that the Palm likelihood estimator for these models is consistent and asymptotically normally distributed.…”

Section: Model Selectionmentioning

confidence: 98%

Bayesian Inference for Non-Markovian Point Processes

Guttorp

Thorarinsdottir

2011

Lecture Notes in Statistics

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Section: Model Selectionmentioning

confidence: 98%

Bayesian Inference for Non-Markovian Point Processes

Guttorp

Thorarinsdottir

2011

Lecture Notes in Statistics

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“…This approach has been widely adopted in many previous articles. Examples include Guan and Loh (2007), Guan and Shen (2010), Waagepetersen andGuan (2009), Guan, Jalilian, andWaagepetersen (2015), Prekešová and Jensen (2013), and Schoenberg (2005).…”

Section: Asymptotic Distributionmentioning

confidence: 99%

Testing First-Order Spherical Symmetry of Spatial Point Processes

Zhang¹,

Mateu²

2020

STAT SINICA

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This article proposes a Kolmogorov-Smirnov-type test to assess spherical symmetry of the first-order intensity function of a spatial point process (SPP).Spherical symmetry, which is an important assumption in the well-known ETAS (epidemic type aftershock sequence) model, means that the intensity function of an SPP is invariant under a spherical transformation in an Euclidean space. An important property of first-order spherical symmetry is that the expected number of points within a sector region is proportional to the angle measure of the region.This provides a way to construct our test statistic. The asymptotic distribution of the test statistic is obtained under the framework of increasing domain asymptotics with weak dependence. We show that the resulting test statistic converges weakly to the absolute maximum of a zero mean Gaussian process under the null hypothesis and it is also consistent under the alternative hypothesis. A simulation study shows that the type I error probability of the test is close to the significance level, and the power increases to one as the magnitude of non-spherical symmetry increases.In an application of the ETAS model to Japan earthquakes, the article concludes that the first-order spherical symmetry assumption can be roughly accepted.

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“…To prove Theorem 4.2 (a), we use the blocking technique introduced by Ibragimov and Linnik (1971) and applied to spatial point processes by Guan and Loh (2007); and Prokešová and Jensen (2013). To this end, we need additional notation.…”

Section: A2 Proof Of Proposition 41mentioning

confidence: 99%

Median-based estimation of the intensity of a spatial point process

Coeurjolly

2015

Ann Inst Stat Math

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This paper is concerned with a robust estimator of the intensity of a stationary spatial point process. The estimator corresponds to the median of a jittered sample of the number of points, computed from a tessellation of the observation domain. We show that this median-based estimator satisfies a Bahadur representation from which we deduce its consistency and asymptotic normality under mild assumptions on the spatial point process. Through a simulation study, we compare the new estimator, in particular, with the standard one counting the mean number of points per unit volume. The empirical study confirms the asymptotic properties established in the theoretical part and shows that the median-based estimator is more robust to outliers than standard procedures.

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Asymptotic Palm likelihood theory for stationary point processes

Cited by 26 publications

References 27 publications

Bayesian Inference for Non-Markovian Point Processes

Bayesian Inference for Non-Markovian Point Processes

Testing First-Order Spherical Symmetry of Spatial Point Processes

Median-based estimation of the intensity of a spatial point process

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