This research project aims to develop new statistical theory, methods and computing algorithms to solve real world problems where the data present unique features such as large volume, large variety and large velocity of change. Traditional methods relying on parametric likelihood functions are no longer feasible for high-dimensional longitudinal data. The PI and her students intend to develop personalized classification strategies for subjects with high heterogeneity variation, and propose to identify subgroups from longitudinal observations through nonparametric random effects estimation. The proposed research also intends to select and optimally combine high-dimensional moment conditions to reduce the dimensionality of large numbers of moment conditions, while retaining the important information from the data to achieve estimation efficiency. In addition, a time-varying network model will be proposed to address dynamic changes of network structures using flexible nonparametric modeling. The proposal also seeks to develop highly efficient computational algorithms for solving optimization problems which involve high-dimensional parameter estimations and matrix operations. The proposed research project will help to tackle fundamental questions in statistical science and will stimulate interest from a large group of scientists in the fields of longitudinal/correlated data analysis, classification, random effects modeling, moment selection, low rank approximation, and time-varying networks for high-dimensional correlated data.
The proposed research topics have many important applications in the biomedical sciences, genomics, environmental sciences, and economics. For example, the personalized classification method is applicable for personalized medicine, where individuals with different biomarkers can receive different medical interventions to get more effective treatment. The time-varying network model is powerful for identifying time-evolving network associations for brain and biological functions, social interaction, and environmental influence over time. In addition, the moment selection method is applicable for panel data in econometrics applications. The PI will integrate the proposed research areas substantially into educational activities through development of new topic courses. The research will also significantly advance undergraduate and graduate students' learning and training.
