Estimation Theory for Semiparametric Models with Bundled Parameters

具有捆绑参数的半参数模型的估计理论

• 批准号: 1007590
• 负责人: Bin Nan
• 金额: $ 20万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007590&HistoricalAwards=false
• 关键词: Estimation; Theory; Semiparametric; Models; Bundled

The investigator proposes extensions of existing asymptotic distributional theories for M- and Z-estimations in the semiparametric models with separated parameters to accommodate situations where the estimation criteria for the semiparametric models are parameterized with bundled parameters, i.e. the infinite dimensional parameter is an unknown function of the parameter of interest. The proposal is motivated by several statistical problems including the efficient estimation in the linear regression model with censored data under several different censoring mechanisms, the efficient estimation in the single index model, the partial likelihood estimation in the Cox regression model with an unknown link function, and the weighted estimation for missing data problems in survival analysis. The investigator also proposes to apply the general theory for bundled parameters to all these problems, particularly for the case that the infinite dimensional nuisance parameter is approximated by regression splines.The proposed research is primarily motivated by PI's collaboration in biomedical studies, where more robust statistical modeling techniques are desirable to reduce the uncertainty of model misspecification, particularly when data are incomplete due to limited study follow-up. The proposed research will also allow the investigator to add more thorough statistical results to the course of advanced survival analysis and be helpful in developing the special topic course on semiparametric models into a regular Ph.D. level course. The proposed research activities will motivate graduate students to become independent researchers who are able to engage in fundamental statistical research.

研究者提出了扩展现有的渐近分布理论的M-和Z-估计的半参数模型与分离的参数，以适应的情况下，估计标准的半参数模型参数化与捆绑参数，即无穷维参数是一个未知的功能的参数的兴趣。该建议的动机是几个统计问题，包括在几种不同的删失机制下的删失数据的线性回归模型中的有效估计，在单指标模型中的有效估计，在考克斯回归模型中的偏似然估计未知的链接函数，和在生存分析中的缺失数据问题的加权估计。研究者还建议将捆绑参数的一般理论应用于所有这些问题，特别是对于无限维滋扰参数近似回归splines的情况。拟议的研究主要是由PI在生物医学研究中的合作推动的，其中更强大的统计建模技术是可取的，以减少模型误指定的不确定性，特别是当由于有限的研究随访而导致数据不完整时。该研究还将使研究者能够在高级生存分析课程中添加更全面的统计结果，并有助于将半参数模型专题课程发展为常规博士学位。水平课程。拟议的研究活动将激励研究生成为能够从事基础统计研究的独立研究人员。