基于充分降维方法的高维数据假设检验问题的研究

项目名称： 基于充分降维方法的高维数据假设检验问题的研究

项目编号： No.11201151

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 於州

作者单位： 华东师范大学

项目金额： 22万元

中文摘要： 随着现代科学技术的发展，数据越来越凸显高维与复杂态势。高维数据频繁见诸于环境科学、医学研究、金融市场以及第二代互联网当中。高维数据给统计学家提出巨大挑战的同时，也给予了统计学界进一步深化发展统计理论与方法的契机。充分降维通过有效将高维变量转化为其低维线性组合，避免了"维数祸根"的困扰，使得进一步统计分析成为可能。本项目致力于通过充分降维方法系统构建并深化高维数据模型下的假设检验理论。我们将着重展开如下三个方面的研究：1）基于二阶参数化降维方法的结构维数检验理论和方法；2）超高维半参数模型下变量显著检验理论和方法；3）高维函数型数据模型的结构维数检验以及特征显著性检验。本项目的研究成果必将为分析和处理金融经济学以及生物信息学等领域所面临的高维数据提供有力的方法保证和理论支持。

中文关键词： 高维；假设检验；变量选择；切片逆回归；充分降维

英文摘要： The scale and complexity of data sets have increased drastically in light of the development in modern technology. High-dimensional data that involve a large amount of variables are nowadays routinely generated and collected in areas such as environmental studies, human health and medical research, financial markets and second-generation internet. High-dimensional data pose many challenges for statisticians and provide considerable momentum in the statistics community to develop new theories and methodologies. Sufficient dimension reduction methodology effectively transforms a high dimensional data problem to a low dimensional one, and thus facilitates many existing statistical methods which used to be hindered by the curse of dimensionality. This project proposes a new paradigm that synthesizes and broadens the theories and methodologies of hypotheses testing for high dimensional data with sufficient dimension reduction methods. We focus mainly on the following three topics: 1) Marginal dimension tests with second order parametric sufficient dimension reduction methods; 2) Testing predcitors contributions based on sufficient dimension reduction methods for ultrahigh dimensional semiparametric models; 3) Deciding the strucutre dimension and feature selection for high dimensional function data based on hypotheses

英文关键词： High Dimensionality；Hypothesis Test；Variable Selection；Sliced Inverse Regression；Sufficient Dimension Reduction