大数据统计分析的模型平均方法

随着大数据时代的到来，大数据背景下的统计估计与推断问题成为当今统计学亟待解决的挑战性问题，本项目拟发展大数据分析的模型平均方法，研究内容包括：简单模型下同质和异质分布式数据分析的模型平均方法研究、复杂统计模型下分布式数据分析的模型平均方法研究、大规模抽样调查数据分析的模型平均方法研究及其应用等，均将提出高效的权重选择准则，特别是结合了抽样设计的权重选择准则，推导新方法的理论性质，包括权重估计的相合性、相应模型平均估计量的渐近最优性及其渐近分布等。本项目的开展将初步建立一套大数据背景下的模型平均理论，为大数据的统计分析提供有力的新工具，从而为各级政府部门、企事业单位的决策提供科学依据。

With the coming of big data era, statistical estimation and inference on big data have become challenging problems needed to be addressed urgently in Statistics. This project aims to develop model averaging methods for big data analysis, including those for distributed data with homogeneity and with heterogeneity under the linear models, respectively, which will be extended to the case of complicated statistical models. Also, model averaging methods taking sampling design into account for large-scale surveys will be investigated. The valid criteria of weight choice will be proposed, and the theoretical properties such as the consistency of weight estimators, asymptotic optimality of the corresponding model averaging estimators and their asymptotic distributions will be derived. With the implementation of this project, the primary theory of model averaging for big data will be built, which will provide a useful tool for big data analysis, and so offer the scientific evidences for making decisions by government departments, enterprises and institutions.