Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

DOI10.3150/13-BEJ523zbMath1312.60062arXiv1410.0180OpenAlexW3098471140MaRDI QIDQ470045

Lothar Heinrich, Sebastian Lück, Volker Schmidt

Publication date: 11 November 2014

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.0180

zbMATH Keywords

\(\beta\)-mixing point process\(\chi^2\)-goodness-of-fit testBoolean modelsempirical Palm mark distributionreduced factorial moment measuressmoothed covariance estimation

Mathematics Subject Classification ID

Non-Markovian processes: estimation (62M09) Generalized stochastic processes (60G20) Non-Markovian processes: hypothesis testing (62M07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (4)

A bound of the \(\beta\)-mixing coefficient for point processes in terms of their intensity functions ⋮ Empirical mark covariance and product density function of stationary marked point processes -- a survey on asymptotic results ⋮ Estimation of entropy for Poisson marked point processes ⋮ Gaussian limits of empirical multiparameter \(K\)-functions of homogeneous Poisson processes and tests for complete spatial randomness

Cites Work

• Empirical mark covariance and product density function of stationary marked point processes -- a survey on asymptotic results
• On estimating the asymptotic variance of stationary point processes
• Empirical distributions in marked point processes
• Mixing: Properties and examples
• Normal approximation for some mean-value estimates of absolutely regular tessellations
• On asymptotic properties of the mark variogram estimator of a marked point process
• Weak and strong convergence of empirical distribution functions from germ-grain processes
• Limiting behavior of U-statistics for stationary, absolutely regular processes
• Asymptotic properties of estimators for the volume fractions of jointly stationary random sets
• Central limit theorem for a class of random measures associated with germ-grain models
• An Introduction to the Theory of Point Processes
• A Nonparametric Test for Spatial Isotropy Using Subsampling
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