Nonparametric Curve Estimation in Presence of Missing Data

存在缺失数据时的非参数曲线估计

• 批准号: 1915845
• 负责人: Sam Efromovich
• 金额: $ 19万
• 依托单位: University of Texas at Dallas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1915845&HistoricalAwards=false
• 关键词: Nonparametric; Curve; Estimation; Presence; Missing

The project focuses on statistical activities motivated by medical and engineering applications in the presence of missing data, a familiar and often inevitable complication in statistical analysis. The first main activity is motivated by the analysis of functional magnet resonance images of the human brain. The project will develop and test statistical procedures that allow doctors and bioengineers to take into account missing data with potential applications in understanding the neural plasticity and developing new methods for diagnosis and treatment of Alzheimer's and Parkinson's diseases. The second main activity is the statistical analysis of radiation and drug therapy of cancer cells and finding efficient treatments for prostate and breast cancers. The third main activity is to develop new statistical methods for time series analysis with environmental applications in wastewater treatment and reducing pollution. The project has the potential for impacts on environmental, actuarial, and cancer and brain studies. Graduate students will participate in the project, and obtained results will be disseminated through publications, presentation at conferences and the distribution of free R packages.The project focuses on several topics in nonparametric curve estimation in the presence of missing data. Firstly, missing may be destructive when based solely on the data no consistent estimation is possible, and then an exploratory sampling is needed to unlock information contained in missing data. The project will develop methodology, theory and methods of efficient (minimal cost) exploratory sampling that allows matching the performance of an oracle that knows the missing mechanism. Secondly, missing always decreases available information. The PI plans to develop theory and methods for the sequential estimation with assigned risk and minimal stopping time, which becomes an attractive and feasible remedy when a priori knowledge of the size of available observations is precluded by missing. Thirdly, the PI plans to develop a shrinking local minimax methodology for missing data and construct a new type of data-driven estimators that can attain the faster minimax rate. Lastly, the project will develop sharp minimax theory and efficient nonparametric estimator for survival analysis in the presence of missing data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目侧重于在缺少数据的情况下开展由医疗和工程应用推动的统计活动，这是统计分析中常见且往往不可避免的复杂问题。第一个主要活动的动机是对人脑的功能磁共振图像进行分析。该项目将开发和测试统计程序，使医生和生物工程师能够考虑丢失的数据，在了解神经可塑性和开发诊断和治疗阿尔茨海默氏症和帕金森氏症的新方法方面具有潜在的应用价值。第二项主要活动是对癌细胞的辐射和药物治疗进行统计分析，并寻找前列腺癌和乳腺癌的有效治疗方法。第三项主要活动是为时间序列分析开发新的统计方法，将环境应用于废水处理和减少污染。该项目可能会对环境、精算、癌症和大脑研究产生影响。研究生将参与该项目，所获得的结果将通过出版物、在会议上的陈述和免费R包的分发来传播。该项目侧重于在存在缺失数据的情况下非参数曲线估计的几个主题。首先，当仅基于数据不可能进行一致估计时，丢失可能是破坏性的，然后需要探索性抽样来解锁丢失数据中包含的信息。该项目将开发有效(最低成本)探索性抽样的方法、理论和方法，使之能够与知道缺失机制的先知的性能相匹配。其次，丢失总是会减少可用信息。PI计划发展分配风险和最小停止时间的序贯估计的理论和方法，当可用观测值的大小的先验知识被遗漏排除时，这成为一种有吸引力的可行的补救措施。第三，PI计划开发一种针对缺失数据的收缩局部极小极大方法，并构造一种新型的数据驱动估计器，以获得更快的极小极大速度。最后，该项目将开发尖锐的极大极小理论和高效的非参数估计器，用于在存在缺失数据的情况下进行生存分析。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。