Nonparametric Curve Estimation in Presence of Missing Data

该项目的重点是在缺失数据的情况下，由医学和工程应用激发的统计活动，这是统计分析中常见的，往往是不可避免的并发症。第一个主要活动是由人脑的功能磁共振图像的分析。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缺失的数据，这些数据在理解神经可塑性和开发诊断和治疗阿尔茨海默病和帕金森病的新方法方面具有潜在的应用。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，并找到有效的前列腺癌和乳腺癌治疗方法。第三项主要活动是为时间序列分析开发新的统计方法，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，并将通过出版物，会议上的演讲和免费R软件包的分发来传播所获得的结果。该项目侧重于缺失数据存在下的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的估计时，缺失可能是破坏性的，然后需要探索性抽样来解锁缺失数据中包含的信息。该项目将开发有效（最低成本）探索性抽样的方法论、理论和方法，使其能够与知道缺失机制的预言机的性能相匹配。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序贯估计的理论和方法，当可用观测值的大小的先验知识因缺失而被排除时，这成为一种有吸引力和可行的补救措施。第三，PI计划开发一种用于缺失数据的收缩局部极大极小方法，并构造一种新型的数据驱动估计器，可以获得更快的极大极小率。最后，该项目将开发尖锐的极大极小理论和有效的非参数估计生存分析在缺失数据的存在。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.