Empirical likelihood and other nonparametric and semiparametric statistical methods for complex surveys, reliability engineering, and environmental studies

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My proposed research focuses on developing fundamental theory and methods of nonparametric and semiparametric inference for survey sampling, reliability engineering, and medical studies. It also addresses modern applied modeling and computational problems in environmental studies, network analysis and big data. It tackles theoretical and computational challenges that arise from these research fields, and aims at providing theoretically sound and practically useful methods. We expect our research outcomes, including novel statistical theory, methods and software, to receive wide attentions from researchers and to be directly employed by scientists and knowledge users for solving practical problems.******The proposed research program is also highly appropriate for training highly qualified personnel (HQP) because it sparks interests from, and poses reasonable challenges to, a wide range of HQP with different backgrounds, and it provides unique opportunities for HQP to build solid mathematical skill, to expose themselves to topical statistical problems, and to explore independently and think critically, among many other essential qualifications.******The proposed research is summarized as follows.******(1) Survey sampling: My goal is to develop effective statistical methods for complex surveys with missing data and for small area estimation (SAE). (a) Missing data are frequently encountered in sample surveys due to non-response. I aim to develop empirical likelihood (EL) and bootstrap-based methods for constructing reliable confidence intervals for population parameters defined by general estimating equations with missing data from complex surveys. (b) SAE is a topic of current interest due to growing demand for reliable small area statistics. I plan to study SAE under informative sampling with an augmented nested-error regression model using penalized B-spline.******(2) EL inference methods: Inference problems for multiple random samples with censored observations are frequently encountered in reliability engineering and medical studies. Statistical models that can effectively borrow strength across multiple samples, such as density ratio models (DRMs), are much preferred for gaining statistical efficiency. I aim to study EL inference based on DRMs, including EL ratio test for comparing quantiles, DRM basis function selection, and EL inference under random-effects DRMs, among many other topics.******(3) Applied stochastic modeling: My objective is to develop theoretically capable and computationally efficient statistical methods for modern network analysis and environmental studies. In particular, I plan to (a) develop spatial-temporal statistical methods for analyzing streaming data from monitoring senor networks or social networks, and (b) study modeling and prediction of sequential biological events for crops of high economic importance in relation to climate change.