基于变系数半参数模型的高维数据统计分析

项目名称： 基于变系数半参数模型的高维数据统计分析

项目编号： No.11301279

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 来鹏

作者单位： 南京信息工程大学

项目金额： 23万元

中文摘要： 高维及超高维数据是当今社会多个领域会经常碰到的数据类型，能否有效的对其进行统计分析具有非常重要的意义。参数模型，常数系数模型越来越无法适应对数据分析的要求。高维以及超高维数据下的变系数类型的半参数模型是本项目研究的重点，该类模型的灵活性使其更能适应于复杂的数据结构。本项目拟对单指标变系数模型从估计有效性、变量选择和模型的识别性问题方面进行研究，在证明其大样本性质的同时，通过数值模拟研究其有限样本性质。本项目还将对超高维数据下变系数类型的半参数模型的降维问题进行研究，给出函数型系数变量的筛选方法，从而进行变量选择，证明筛选方法的相合性，并研究混合函数型系数与常数系数变量的模型的变量筛选及筛选方法的相合性，通过数值模拟研究其有限样本性质。

中文关键词： 半参数模型；变量选择；有效性；超高维；特征筛选

英文摘要： High dimensional data and ultrahigh-dimensional data are often encountered in many different areas in our social lives. It is meaningful to do statistical analysis effectively to these types of data. For the parametric models and constant coefficient models, they are increasingly unable to meet the requirement of data analysis. This project will focus on studying the varying-coefficient semiparametric models with high dimensional and ultrahigh-dimensional data. This kind of models is flexible so that it can adapt to the complex data structure. This project aims to study the estimation efficiency, variable selection procedure and model identification problems for the single-index varying-coefficient models. It will give the proof of the large sample properties, and complete the numerical simulations to verify the finite sample properties. On the other hand, this project will also study the dimension reduction problem for the varying-coefficient semiparametric models with ultrahigh-dimensional data. The screening methods for screening the functional coefficient variables are proposed, thus the general variable selection procedure is proceeded. The consistent property of the screening method will be proved. Furthermore, this project aims to study on the consistency of the screening method for the model which have m

英文关键词： Semiparametric model；variable selection；efficiency；ultrahigh dimension；feature screening