Substationarity for spatial point processes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:171

Article

Zhang, Tonglin¹  Mateu, Jorge² 

[1] Purdue Univ, Dept Stat, 250 North Univ St, W Lafayette, IN 47907 USA

[2] Univ Jaume 1, Dept Matemat, Campus Riu Sec, Castellon de La Plana 12071, Spain

关键词: Intensity functions;    Kernel methods;    Nonstationarity;    Semiparametric estimation;    Spatial point processes;    Substationarity;   

DOI  :  10.1016/j.jmva.2018.11.001

来源: Elsevier

【 摘 要 】

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 semi parametric 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free