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Statistical Analysis of Spatio-Temporal Data: its Theory and Applications

时空数据统计分析：理论与应用

基本信息

批准号：
15200021
负责人：
YAJIMA Yoshihiro
金额：
$ 31.2万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15200021/
关键词：
Spatio-temporal random field Markov random field Spatio-temporal point process Empirical Bayes estimator Spatial competition Spatial data analysis Circular data analysis Small area statistics 空間フーリエ解析 Echelon解析角度データ解析空間的分散不均一性時空

项目摘要

We held a research conference on spatio-temporal statistical analysis every year through the research period from 2003 to 2006. These conferences have made much contribution to the development of spatio-temporal statistical analysis in both theory and its applications and to that the researchers in this field are able to deepen the understanding of the topic and share the studies to be solved in future with each other.We have conducted our research project by dividing the members into five groups. First for inference theory and applications of random fields, we proposed a generalization of Fourier analysis of time series to spatio-temporal data and applied it to analyze a land price data of Tokyo Metropolitan area. Secondly for inference theory and its applications of spatio-temporal point processes, we developed an intensity function taking into account of spatio and temporal correlations simultaneously and applied it to analyze earthquake data. Furthermore we developed a threshold method to predict the sample variance and applied it to analyze rainfall data. Spatio-temporal correlation analysis between epidemiological data was also conducted. Thirdly for inference theory and applications of large sample-size data, we developed a new methodology of dscriminat analysis on Markov random fields and Echelon method for detecting hot spots of spatial data. Fourthly for inference theory and its application of small area data, we developed minimax and empirical Bayes estimators, which are able to overcome multicolinearity, and are robust against the instability caused by small sample size data. Finally for inference theory and its applications of panel data, we conducted an empirical analysis of spatial competition and its equiburium. And we conducted simulation studies, which investigated spurious spatial correlation caused by autocorrelations within individual time series and spatial heteroskedasticity between individual time series.

从2003年到2006年，我们每年都举行一次时空统计分析研究会议。这些会议对时空统计分析的理论和应用的发展做出了很大的贡献，使该领域的研究人员能够加深对该主题的理解，并相互分享未来需要解决的研究问题。我们将成员分为五个小组进行我们的研究项目。首先，从随机场的推理理论和应用出发，将时间序列的傅立叶分析推广到时空数据，并应用于东京都地价数据的分析。其次，在时空点过程的推理理论及其应用方面，我们提出了一种同时考虑空间和时间相关性的强度函数，并将其应用于地震数据的分析。此外，我们发展了一个阈值方法来预测样本方差，并将其应用于分析降雨数据。流行病学资料之间的时空相关性也进行了分析。第三，在大样本数据的推理理论与应用方面，提出了马尔可夫随机场的离散分析方法和空间数据热点检测的阶梯方法。第四，在小区域数据的推断理论及其应用方面，我们发展了Minimax和经验Bayes估计，它们能够克服多重共线性，并且对小样本数据引起的不稳定性具有鲁棒性。最后运用面板数据的推理理论和应用，对空间竞争及其均衡进行了实证分析。我们进行了模拟研究，研究了虚假的空间相关性所造成的自相关性在个别时间序列和空间异方差之间的个别时间序列。