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发展调查抽样，可靠性工程和医学研究的非参数和半参数推断的基本理论和方法。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和实用的方法。我们期望我们的研究成果，包括新的统计理论，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。 拟议的研究计划也非常适合培养高素质人才（HQP），因为它激发了兴趣，并提出了合理的挑战，广泛的HQP具有不同的背景，它提供了独特的机会，为HQP建立坚实的数学技能，暴露自己的专题统计问题，并独立探索和批判性思考，在许多其他必要的资格。 拟议的研究总结如下。 (1)调查抽样：我的目标是为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。(a)在抽样调查中，由于没有答复，经常会遇到数据缺失的情况。我的目标是开发经验似然（EL）和引导为基础的方法来构建可靠的置信区间的人口参数定义的一般估计方程与复杂的调查缺失数据。(b)由于对可靠的小区域统计数据的需求不断增长，SAE是当前感兴趣的主题。我计划在信息抽样下使用惩罚B样条的增强嵌套误差回归模型研究SAE。 (2)EL推断方法：在可靠性工程和医学研究中，经常遇到具有截尾观测的多个随机样本的推断问题。可以有效地在多个样本之间借用强度的统计模型，例如密度比模型（DRM），对于获得统计效率来说是非常优选的。我的目标是研究基于DRM的EL推理，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推理，以及许多其他主题。 (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交网络的流数据，（B）研究建模和预测与气候变化相关的高经济重要性作物的连续生物事件。

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.