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

用于复杂调查、可靠性工程和环境研究的经验可能性和其他非参数和半参数统计方法

• 批准号: RGPIN-2017-06267
• 负责人: Cai, Song
• 金额: $ 1.38万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=710812
• 关键词: Empirical; likelihood; other; nonparametric; semiparametric

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.

我提出的研究重点是开发基本理论和非参数和半参数推断的方法，用于调查采样，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引起的理论和计算挑战，并旨在提供理论上的声音和实际上有用的方法。我们希望我们的研究成果，包括新颖的统计理论，方法和软件，将受到研究人员的广泛关注，并将受到科学家和知识使用者的直接利用，以解决实际问题。 拟议的研究计划也非常适合培训高素质的人员（HQP），因为它引发了具有不同背景的广泛HQP的兴趣，并提出了合理的挑战，它为HQP提供了独特的机会来建立坚实的数学技能，在许多其他基本资格中，将自己暴露于局部统计问题，独立探索并进行批判性思考。 拟议的研究总结如下。 （1）调查抽样：我的目标是开发有效的统计方法，用于缺少数据和小面积估计（SAE）的复杂调查。 （a）由于无响应，在样本调查中经常遇到丢失的数据。我的目标是开发经验可能性（EL）和基于自举的方法，用于构建可靠的置信区间，以通过一般估计方程定义的人口参数，而复杂调查中缺少数据。 （b）由于对可靠的小面积统计数据的需求不断增长，SAE是当前感兴趣的话题。我计划使用惩罚B-Spline的增强嵌套回归模型来研究SAE。 （2）EL推理方法：在可靠性工程和医学研究中经常遇到多个随机样本的推理问题。可以有效地借用多个样品（例如密度比模型（DRM））的强度的统计模型，在获得统计效率方面非常喜欢。我的目标是基于DRM的EL推断，包括在随机效应的DRM中比较分位数，DRM基函数选择和EL推断的EL比率测试，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能力和计算有效的统计方法。特别是，我计划（a）开发空间统计方法，用于分析监测索诺网络或社交网络的流数据，以及（b）研究对序列生物事件的建模和预测，以实现与气候变化相关的高经济重要性的作物。