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.

我们每年在2003年至2006年的研究期间举办一次有关时空统计分析的研究会议。这些会议为理论及其应用中的时空统计分析做出了很大贡献领域能够加深对主题的理解，并分享将来将来要解决的研究。我们通过将成员分为五组来进行我们的研究项目。首先，对于推理理论和随机领域的应用，我们提出了对时空数据的傅立叶分析的概括，并将其应用于东京大都市地区的土地价格数据。其次，对于推理理论及其在时空点过程中的应用，我们同时考虑了时空相关性，并将其应用于分析地震数据。此外，我们开发了一种阈值方法来预测样品方差并将其应用于分析降雨数据。还进行了流行病学数据之间的时空相关分析。第三，对于推理理论和大型样本大小数据的应用，我们开发了一种针对马尔可夫随机字段和梯队检测空间数据热点的dscriminat分析的新方法。对于推理理论及其应用小面积数据的第四，我们开发了最小值和经验贝叶斯估计量，这些估计量能够克服多种线性，并且对小样本量数据引起的不稳定性很强。最后，对于推断理论及其对小组数据的应用，我们对空间竞争及其e骨进行了经验分析。我们进行了仿真研究，该研究研究了单个时间序列中的自相关和个体时间序列之间的空间异质性引起的虚假空间相关性。