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

我建议的研究重点是为调查抽样、可靠性工程和医学研究开发非参数和半参数推理的基本理论和方法。它还解决了环境研究、网络分析和大数据中的现代应用建模和计算问题。它解决了这些研究领域中出现的理论和计算挑战，旨在提供理论上合理且实际有用的方法。我们期望我们的研究成果，包括新颖的统计理论、方法和软件，得到研究人员的广泛关注，并直接被科学家和知识使用者用于解决实际问题。

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.