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

在2003年至2006年的研究期间，我们每年召开一次时空统计分析研究会议。这些会议对时空统计分析在理论和应用上的发展做出了很大的贡献，也使这一领域的研究人员能够加深对这一主题的理解，并相互分享未来有待解决的研究。我们把成员分成五组来进行研究项目。首先在随机场的推理理论和应用方面，提出了将时间序列的傅里叶分析推广到时空数据中，并将其应用于东京大都市区的地价数据分析。其次，在时空点过程的推理理论及其应用方面，我们建立了同时考虑时空相关性的强度函数，并将其应用于地震数据分析。在此基础上，提出了一种预测样本方差的阈值方法，并将其应用于降雨数据分析。并对流行病学资料进行时空相关性分析。第三，针对大样本数据的推理理论和应用，提出了基于马尔可夫随机场的判别分析方法和用于空间数据热点检测的梯队方法。第四，对于小面积数据的推理理论及其应用，我们开发了极大极小贝叶斯估计和经验贝叶斯估计，它们能够克服多重共线性，并且对小样本量数据引起的不稳定性具有鲁棒性。最后，对面板数据的推理理论及其应用进行了空间竞争及其均衡的实证分析。我们进行了模拟研究，研究了个体时间序列内部自相关引起的伪空间相关和个体时间序列之间的空间异方差。

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.