Composite Resampling Inference for Dependent Data

目前用于相关数据分析的统计方法往往依赖于指定一个适当的模型，这在实践中可能很困难。一个潜在的后果是，从一个不恰当或错误的模型中得出的结论可能是不可靠的或误导性的。该项目旨在开发有效和准确的统计方法，这些方法是“无模型”的，或者在应用时不需要对数据的依赖性进行限制性假设。这项研究的一个直接好处是为统计推断提供了不受模型选择或模型错误规范影响的替代工具。因此，该研究将有利于环境学、经济学、地质学和天文学等科学领域的基于数据的推理，这些领域遇到不同形式的依赖数据，并且无模型方法可以在数据分析中发挥重要作用。该计划亦会透过研究生辅导及与本地大专院校本科生的外展活动，支持学生的专业发展，以促进统计及数据科学方面的招聘和教育。该项目特别旨在生成复合或混合类型的重新采样方法，这些方法结合了重用依赖数据的策略。通过合并哲学上不同的重采样技术（子采样和bootstrap）， PI将研究非参数推理的卷积子采样。这种新的重采样方法适用性广，在温和条件下具有良好的性能。对于重要类型的强依赖或长期依赖时间序列，统计推断在很大程度上依赖于未知过程指数。PI将研究长记忆下的重采样，并通过重采样思想的组合来开发该指数的第一个估计。此外，PI将为时间序列和空间数据开发新的经验似然方法，通过结合不同的重采样设备（数据转换和数据阻塞）来推断各种依赖结构。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Current statistical methodology for dependent data analysis often relies on specifying an adequate model, which can be difficult in practice. A potential consequence is that conclusions drawn from an inappropriate or mistaken model may be unreliable or misleading. The project seeks to develop efficient and accurate statistical methods that are "model-free" or apply without restrictive assumptions about the dependence in data. A direct benefit of this research will be to provide alternative tools for statistical inference that are not susceptible to model choice or model misspecification. Therefore, the research will benefit data-based inference in scientific areas such as environmetrics, economics, geology, and astronomy, which encounter different forms of dependent data and where model-free methods can play an important role in data analysis. The project will also support the professional development of students through graduate student mentoring as well as outreach activities with undergraduate students at local colleges and universities for promoting recruitment and education in statistics and data science.This project particularly aims to produce composite, or hybrid-type, resampling methods that combine strategies for re-using dependent data. By merging philosophically different resampling techniques (subsampling and bootstrap), the PI will investigate convolved subsampling for nonparametric inference. This new resampling method has wide applicability and favorable performance under mild conditions. For important types of strongly or long-range dependent time series, statistical inference depends heavily on an unknown process index. The PI will study resampling under long-memory and develop a first-ever estimator of this index via a composition of resampling ideas. Additionally, the PI will develop new empirical likelihood methods for time series and spatial data by combining different resampling devices (data transformations and data blocking) for inference over a variety of dependence structures.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.