高维稀疏统计模型中的变量选择与检验

项目名称： 高维稀疏统计模型中的变量选择与检验

项目编号： No.11471223

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 崔恒建

作者单位： 首都师范大学

项目金额： 65万元

中文摘要： 关于高维数据的变量选择方法目前还处在变量的选择与估计阶段，而缺乏统计检验功能，对于高维稀疏数据模型下的统计检验以及超高维数据下的快速变量降维方法也甚少。本项目拟在这两个统计学基础课题上开展深入研究，并有望取得突破性成果。具体我们将在带有附加信息的高维高维稀疏数据的变量选择方法上提出既能选择与估计，同时又能进行统计检验的新方法；提出高维稀疏数据的聚类降维新理论和技术；提出超高维稀疏数据下的扫描的新理论和方法。这些新的高维复杂数据的分析方法可应用于CT检测成像，GWAS等数据分析中去、为信息技术、生物医学等研究领域提供先进的数据分析方法，丰富高维复杂数据的统计理论和分析方法。

中文关键词： 变量选择；统计检验；高维模型；参数估计；稳健方法

英文摘要： It is well known that variables selection approach in high dimensional data analysis is in stage of the selecting variables and parameter estimation which is lack of statistical testing for some interested variables. Meanwhile, there are few statistical testing methods for the statistical model of high dimensional data with sparse case as well as fast dimension reduction method for ultra-high dimension data. This project will explore some new methods in these two fundamental statistical problems, and hopefully to establish some new methodologies and theory, which including three aspects as following. 1. Find out some new methods not only for selecting variables, but also for estimation, and at same time for statistical testing of interested variables in the high dimensional data with sparse case and auxiliary information. 2. Propose some new theory and techniques for cluster dimension reduction in high-dimensional data with sparse case. 3. Propose some new theory and methods for feature screening in ultra-high dimensional data with sparse case. These new methods for high dimensional and complicate data analysis can be used to image CT detection and imaging, GWAS data analysis and so on, it will also provide advanced data analysis methods in some application fields, such as information, biomedicine sciences, and enrich data analysis theory and methodologies.

英文关键词： Variable selection;Statistical test;High-dimensional model;Parametric estimation;Robust method