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

我建议的研究集中在发展非参数和半参数推理的基本理论和方法，用于调查抽样、可靠性工程和医学研究。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，旨在提供理论上可靠和实际有用的方法。我们期待我们的研究成果，包括新颖的统计理论、方法和软件，受到研究人员的广泛关注，并直接被科学家和知识用户用于解决实际问题。 拟议的研究计划也非常适合培养高素质人才(HQP)，因为它激发了来自不同背景的广泛HQP的兴趣，并对他们提出了合理的挑战，它为HQP提供了独特的机会，让他们建立扎实的数学技能，接触专题统计问题，独立探索和批判性思考，以及许多其他基本资格。 拟开展的研究工作总结如下。 (1)调查抽样：我的目标是为有缺失数据的复杂调查和小区域估计(SAE)开发有效的统计方法。(一)在抽样调查中，由于没有答复，经常会出现数据遗漏的情况。我的目标是开发基于经验似然(EL)和Bootstrap的方法，以构建由带有复杂调查中缺失数据的一般估计方程定义的总体参数的可靠可信区间。(B)由于对可靠的小区域统计数据的需求日益增长，小面积气候变化是目前人们感兴趣的一个专题。我打算在信息抽样下，利用惩罚B-样条法建立一个增广的嵌套误差回归模型来研究SAE。 (2)EL推断方法：在可靠性工程和医学研究中经常遇到带有截尾观测的多个随机样本的推断问题。可以有效地跨多个样本借用强度的统计模型，如密度比模型(DRM)，是获得统计效率的首选。我的目标是研究基于DRM的EL推断，包括比较分位数的EL比率检验、DRM基函数的选择以及随机效应DRM下的EL推断等。 (3)应用随机建模：我的目标是为现代网络分析和环境研究开发理论上有能力和计算效率高的统计方法。特别是，我计划(A)开发时空统计方法，用于分析来自监测传感器网络或社会网络的流数据，以及(B)研究对气候变化具有高度经济重要性的作物的连续生物事件的建模和预测。

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.