随机右删失数据半参数回归模型的光滑FIC平均估计理论及其应用

项目名称： 随机右删失数据半参数回归模型的光滑FIC平均估计理论及其应用

项目编号： No.11301561

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： 孙志猛

作者单位： 中央财经大学

项目金额： 22万元

中文摘要： 模型选择是数据建模的关键环节，是统计学热点课题，而包含其为特例的模型平均问题是目前统计学国际前沿课题。目前模型平均方法的研究成果主要针对简单随机样本，尚不能有效解决现代应用领域常见的删失数据。申请者前期研究表明，异常值对模型平均估计的效果有显著影响，且在不同分位数水平上，协变量对响应变量影响不同，因此，为了全面描述响应变量分布特征，不仅需要考虑协变量对响应变量中心的影响，还应考虑对其他分位数的影响。本科题拟基于前期基础,借鉴FIC准则，结合随机右删失数据结构特点，针对半参数模型，分别从均值建模和分位数建模的角度，使用纠偏技术，运用B样条、鞅、凸引理和矩阵伦等理论工具，系统性建立随机右删失数据的模型平均估计理论体系，并深入发展针对单个兴趣参数的传统FIC准则，突破性解决兴趣向量的平均估计问题；把理论成果应用于实际数据分析。本项目内容不仅对数据分析具有重要理论意义，也将为应用领域提供有效工具。

中文关键词： 缺失数据；删失数据；模型平均；网络结构数据；半参数模型

英文摘要： Model selection is clearly crucial to statistical modeling and has been one of the hot topics in statistics. Model averaging approach, which includes model selection as one of its special case,is the frontier of statistical theory in an international context.Until now, research on model averaging has achieved remarkable results. However, most of these research were undertaken with independent identically distributed sample, and did not work for censored data which is common in real applications. What's more, preliminary research of the applicant shew that outliers might have significant impact on traditional model averaging method and the covariates affected the response differently in different quantile levels. Thus , to depict the character of the distribution of the response, one not only has to consider the influence of the covariates on the center of the response,but also infulence on other quantiles. In this project, on basis of the preliminary research, by means of the FIC criterion,combining the sepcial structure of randomly right censored data,in virtue of B-spline,martingale,the convexity lemma, matrix theory and bias-corrected techniques, we intend to systemicall build model averaging theory for semiparametric regression model with randomly right censored response via mean regression as well as quanti

英文关键词： Missing data；Censored data；Model averaging；Network data；Semiparametric model