Substationarity for spatial point processes
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https://doi.org/10.1016/j.jmva.2018.11.001 |
Metadata
Title
Substationarity for spatial point processesDate
2019-05Publisher
Elsevier Inc.ISSN
0047-259XBibliographic citation
Zhang, T., & Mateu, J. (2019). Substationarity for spatial point processes. Journal of Multivariate Analysis, 171, 22-36.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
This article aims to introduce the concept of substationarity for spatial point processes
(SPPs). Substationarity is a new concept that has never been studied in the literature. Substationarity means that the distr ... [+]
This article aims to introduce the concept of substationarity for spatial point processes
(SPPs). Substationarity is a new concept that has never been studied in the literature. Substationarity means that the distribution of an SPP can only be invariant under location shifts
within a linear subspace of the domain. This notion lies theoretically between stationarity
and nonstationarity. To formally propose the approach, the article provides the definition of
substationarity and estimation of the first-order intensity function, including the subspace.
As this may be unknown, we recommend using a parametric method to estimate the linear
subspace and a nonparametric one to estimate the first-order intensity function given the
linear subspace. It is thus a semiparametric approach. The simulation study shows that both
the estimators of the linear subspace and the first-order intensity function are reliable. In an
application to a Canadian forest wildfire data set, the article concludes that substationarity
of wildfire occurrences may be assumed along the longitude, indicating that latitude is a
more important factor than longitude in Canadian forest wildfire studies. [-]
Is part of
Journal of Multivariate Analysis, Vol. 171 (may 2019)Rights
© 2018 Elsevier Inc. All rights reserved.
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