Nonparametric Curve Estimation in Presence of Missing Data

University Of Texas At Dallas, Richardson TX

Investigators

Abstract

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.