Inhomogeneous higher-order summary statistics for point processes on linear networks
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https://doi.org/10.1007/s11222-020-09942-w |
Metadatos
Título
Inhomogeneous higher-order summary statistics for point processes on linear networksFecha de publicación
2020Editor
SpringerISSN
0960-3174; 1573-1375Cita bibliográfica
CRONIE, Ottmar; MORADI, Mehdi; MATEU, Jorge. Inhomogeneous higher-order summary statistics for point processes on linear networks. Statistics and computing, 2020Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://link.springer.com/article/10.1007/s11222-020-09942-wVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
As a workaround for the lack of transitive transformations on linear network structures, which are required to consider different notions of distributional invariance, including stationarity, we introduce the notions ... [+]
As a workaround for the lack of transitive transformations on linear network structures, which are required to consider different notions of distributional invariance, including stationarity, we introduce the notions of pseudostationarity and intensity reweighted moment pseudostationarity for point processes on linear networks. Moreover, using arbitrary so-called regular linear network distances, e.g. the Euclidean and the shortest-path distance, we further propose geometrically corrected versions of different higher-order summary statistics, including the inhomogeneous empty space function, the inhomogeneous nearest neighbour distance distribution function and the inhomogeneous J-function. Such summary statistics detect interactions of order higher than two. We also discuss their nonparametric estimators and through a simulation study, considering models with different types of spatial interaction and different networks, we study the performance of our proposed summary statistics by means of envelopes. Our summary statistic estimators manage to capture clustering, regularity as well as Poisson process independence. Finally, we make use of our new summary statistics to analyse two different datasets: motor vehicle traffic accidents and spiderwebs. [-]
Publicado en
Statistics and computing, 2020Proyecto de investigación
J. Mateu is funded by Grant MTM2016-78917-R from the Spanish Ministry of Economy and Competitivity.Derechos de acceso
© Springer Science+Business Media, LLC, part of Springer Nature 2020
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http://rightsstatements.org/vocab/InC/1.0/
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