复杂数据下含指标项半参数模型结构的统计推断及应用

项目名称： 复杂数据下含指标项半参数模型结构的统计推断及应用

项目编号： No.11471160

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： 黄振生

作者单位： 南京理工大学

项目金额： 68万元

中文摘要： 含指标项半参数模型主要包括具有代表性的单指标模型和单指标部分线性模型。现有的研究都是建立在给定或已知模型结构的条件下进行的统计推断，但是这种假定常常是不真实的，在诸如缺失和测量误差数据等复杂数据问题中这一问题尤为突出，然而这一重要问题的研究仍未得到很好解决。为此，此课题研究复杂数据下含指标项半参数模型结构的推断问题。具体内容为：1)使用SCAD(Smoothly Clipped Absolute Deviation Penalty)等方法研究线性参数部分结构的选择问题；2)使用SCAD等方法研究非线性部分的指标参数部分结构的选择问题；3)使用广义似然比和经验似然比等方法研究上述1)和2)两种情况下的非参数部分的结构选择问题；4)建立上述所有推断方法的理论基础,并研究此类模型的应用问题，即研究SCAD 估计、两类似然比推断统计量的渐近分布、收敛速度等大样本性质和应用到相关领域方法。

中文关键词： 复杂数据；指标项；半参数回归模型；结构选择；渐进分布

英文摘要： Semiparametric regression models with index include the popular single-index model and partially linear single-index model.In the existing research,the authors often assume that the model structures are given or known and further make statistical inferences based on those structures.But,these assumptions are not real in the real examples and one can not expect their rationality in complex data sets such as missing data and measure-error data and so on.This is an important and yet largely unsolved problem for the current models.To this end, we study the statistical inferences for semiparametric model structure with index under complex data set in this project.The details are stated as follows: 1) study parametric structure selection for linear parts by using the smoothly clipped absolute deviation penalty (SCAD) and so on; 2) study index parametric structure selection for the nonparametric part by using the SCAD and so on; 3) study the functional structure selection for the two cases of the expressions 1) and 2) by using the generalized likelihood ratio and the empirical likelihood ratio method and so on; 4) study the asymptotic distributions for the above inferences and study the application issues of the current models,that is to say, study the large sample properties on the foregoing statistics, such as the asymptotic distributions and the convergence rate for the SCAD estimates and the above two type of likelihood ratio statistics,and so on, and discuss their application problems in the relevant fields.

英文关键词： Complex data;Index;Semiparametric regression models;Structure selection;Asymptotic distributions