Nonparametric Curve Estimation in Presence of Missing Data

该项目的重点是在数据缺失的情况下，由医学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情况。第一个主要活动是由分析人类大脑的功能性磁共振图像引起的。该项目将开发和测试统计程序，使医生和生物工程师能够在理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病的新方法时，考虑到缺失的数据的潜在应用。第二项主要活动是对癌细胞的放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。第三项主要活动是发展新的统计方法，进行时间序列分析，并将其应用于废水处理和减少污染。该项目有可能对环境、精算、癌症和大脑研究产生影响。研究生将参与该项目，获得的成果将通过出版物、会议演示和免费分发R包的方式传播。该项目主要关注在缺失数据存在下的非参数曲线估计中的几个主题。首先，当仅基于数据而无法进行一致性估计时，缺失可能是破坏性的，然后需要探索性采样来解锁缺失数据中包含的信息。该项目将开发有效（最小成本）探索性抽样的方法论、理论和方法，以匹配知道缺失机制的oracle的性能。其次，缺失总是减少可用信息。PI计划开发具有指定风险和最小停止时间的顺序估计的理论和方法，当可用观测值的大小的先验知识因缺失而被排除时，这将成为一种有吸引力和可行的补救措施。第三，PI计划针对缺失数据开发一种缩小的局部极小极大方法，并构建一种能够获得更快极小极大率的新型数据驱动估计器。最后，该项目将开发尖锐极小极大理论和有效的非参数估计，用于存在缺失数据的生存分析。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.