高维数据的空间变系数模型研究

项目名称： 高维数据的空间变系数模型研究

项目编号： No.11271242

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 孙燕

作者单位： 上海财经大学

项目金额： 60万元

中文摘要： 在特定空间范围内进行的经济活动或行为往往兼具空间依赖性和空间异质性的特征，这给变量之间关系的空间建模带来了挑战。另外，由于空间经济变量之间关系的错综复杂性，影响响应变量的解释变量个数往往是高维的，背离了通常分析中解释变量个数有限的假定。而正确认识变量之间的关系有助于我们的决策。因此，本项目将探讨高维空间数据的建模及相关问题的处理，提出了体现空间数据特征的空间变系数模型，该类模型具有广阔的应用前景。主要研究内容有：有限维解释变量的空间变系数模型的变量选择和估计理论，为高维情形下的研究提供基础和思路；解释变量维数小于样本容量但趋于无穷的高维情形下模型的变量选择和估计理论；解释变量个数大于样本容量的超高维情形下的变量选择和估计理论；还将研究空间变系数模型一种特例的有限维和高维情形下的变量选择和估计；同时本课题的研究将始终注重模型及方法在诸如我国地区经济增长因素和空间带动性等实际问题分析中的应用。

中文关键词： 空间自相关；空间变系数模型；异方差；模型选择；经济实证分析

英文摘要： Economic activities happened in given space usually shows characteristics of spatial dependence and heterogeneity, it presents a challenge to spatial modeling of relationships between variables. Moreover, because of complications of economic relationships in space, the dimensionality of explanatory variables affecting response variable is always high. It departs from the usual assumption of finite dimensionality of explanatory variables. However, accurately understanding the relationships between variables helps us to make correct decisions. So, this project will study the modeling aspect of high dimensional spatial data and solution methods of related problems, and propose the spatially varying coefficient model which can reflect the features of spatial data. The proposed model envisions a wide application. The research includes the theory of variable selection and estimation of spatially varying coefficient model with finite dimensional covariates, which provides the basises and ideas on the study of high dimensional covariates, the theory of variable selection and estimation of high dimensional situation where the number of explanatory variables is larger than sample size and convergs to infinity, the related theory under ultra high dimensional covariates, and the theory under a special case of spatially vary

英文关键词： spatial correlation；spatially varying coefficient model；heteroskedasticity；model selection；economic emipiral analysis