Multivariate Hawkes processes with spatial covariates for spatiotemporal event data analysis

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Chenlong Li, Kaiyan Cui
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引用次数: 0

Abstract

Spatiotemporal events occur in many disciplines, including economics, sociology, criminology, and seismology, with different patterns in space and time related to environmental characteristics, policing, and human behavior. In this paper, we propose a class of multivariate Hawkes processes with spatial covariates to consider the influence structure of spatial features in spatiotemporal events and the spatiotemporal patterns such as clustering. Baseline intensities are assumed to be a spatial Poisson regression model to explain spatial feature influence. The transfer functions are considered unknown but smooth and decreasing to explain the clustering phenomena. A semiparametric estimation method based on time discretization and local constant approximation is introduced. Transfer function estimators are shown to be consistent, and baseline intensity estimators are consistent and asymptotically normal. We examine the numerical performance of the proposed estimators with extensive simulation and illustrate the application of the proposed model to crime data obtained from Pittsburgh, Pennsylvania.

Abstract Image

Abstract Image

带有空间协变量的多变量霍克斯过程,用于时空事件数据分析
时空事件发生在经济学、社会学、犯罪学和地震学等许多学科中,其不同的时空模式与环境特征、治安和人类行为有关。在本文中,我们提出了一类带有空间协变量的多变量霍克斯过程,以考虑时空事件中空间特征的影响结构以及集群等时空模式。基线强度被假定为空间泊松回归模型,以解释空间特征的影响。传递函数被认为是未知的,但平滑且递减,以解释聚类现象。引入了一种基于时间离散化和局部常数近似的半参数估计方法。结果表明,传递函数估计值是一致的,基线强度估计值也是一致的且渐近正态的。我们通过大量仿真检验了所提出的估计器的数值性能,并将所提出的模型应用于宾夕法尼亚州匹兹堡市的犯罪数据。
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来源期刊
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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