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2017 Gradient angle-based analysis for spatiotemporal point processes
Tonglin Zhang, Yen-Ning Huang
Electron. J. Statist. 11(2): 4424-4451 (2017). DOI: 10.1214/17-EJS1368


Spatiotemporal point processes (STPPs) are important in modeling randomly appeared events developed in space and time. Statistical methods of STPPs have been widely used in applications. In all of these methods, evaluations and inferences of intensity functions are the primary issues. The present article proposes a new method, which attempts to evaluate angles of gradient vectors of intensity functions rather than the intensity functions themselves. According to the nature of many natural and human phenomena, the evaluation of angle patterns of the gradient vectors is more important than the evaluation of their magnitude patterns because changes of angle patterns often indicate global changes of these phenomena. This issue is investigated by simulation studies, where significant variations of gradient angle patterns are identified only when modes of intensity functions are changed. To study these phenomena, the article proposes an analysis method for gradient angles of the first-order intensity function of STPPs. The proposed method is used to analyze aftershock earthquake activities caused by great mainshock earthquakes occurred in Japan 2011 and Indian Ocean 2004, respectively, where a significant global change in the second case is identified.


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Tonglin Zhang. Yen-Ning Huang. "Gradient angle-based analysis for spatiotemporal point processes." Electron. J. Statist. 11 (2) 4424 - 4451, 2017.


Received: 1 December 2015; Published: 2017
First available in Project Euclid: 17 November 2017

zbMATH: 06816621
MathSciNet: MR3724485
Digital Object Identifier: 10.1214/17-EJS1368

Primary: 62M30
Secondary: 62G05 , 62G20

Keywords: Berman-Diggle estimator , Gradient angles , gradient vectors , intensity functions , kernel functions , spatiotemporal point processes


Vol.11 • No. 2 • 2017
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