CAREER: Bootstrap M-estimation in Semi-Nonparametric Models

职业：半非参数模型中的 Bootstrap M 估计

• 批准号: 1151692
• 负责人: Guang Cheng
• 金额: $ 40万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1151692&HistoricalAwards=false
• 关键词: CAREER; Bootstrap; estimation; Semi; Nonparametric

The PI deals with the bootstrap inferential strategies for two broad classes of bootstrap methods in the context of semi-nonparametric models. As a general-purpose approach to statistical inferences, the bootstrap has found wide applications in semi-nonparametric models. Unfortunately, systematic theoretical studies on the bootstrap inferences are extremely limited, especially when the nonparametric component is not root-n estimable. Two classes of bootstrap methods are considered: the exchangeably weighted bootstrap (EWB) and the model-based bootstrap (also known as the parametric bootstrap). The PI proves that the EWB consistently estimates the asymptotic variance of the Euclidean estimate and is theoretically valid in drawing semiparametric inferences in the framework of penalized M-estimation. However, the EWB may become invalid in drawing inferences for nonparametric components. Hence, the PI considers the model-based bootstrap, and theoretically justifies it as an universally valid inference procedure for all the parameters in semi-nonparametric models. The proposed research also involves the development of advanced empirical processes tools. The above research lays the theoretical foundation for the general semi-nonparametric inferences via various bootstrap sampling schemes, and establishes a general framework for non-standard asymptotic theory concerning the nonparametric components.The immediate need for fast and efficiently extracting information from all the dimensions of modern massive data sets gives rise to the increasing popularity of the semi-nonparametric models. For example, to understand the recent financial crisis, the semi-nonparametric copula models are applied to address tail dependence among shocks to different financial series and also to recover the shapes of the impact curve for individual financial series. The proposed research promotes the use of semi-nonparametric models in analyzing modern complex data by developing a series of innovative and valid bootstrap inferential tools, and eventually gain substantial scientific productivity across various disciplines. Statistical science benefits from the increasing number of researchers trained in semi-nonparametric modelling both from the statistical and scientific viewpoints. This would include the students funded by this work, broader collaborating research and educational activities. The above research also produces easy-to-implement software for the public.

PI 处理半非参数模型背景下两大类引导方法的引导推理策略。作为统计推断的通用方法，引导程序在半非参数模型中得到了广泛的应用。不幸的是，关于引导推论的系统理论研究极其有限，特别是当非参数分量不可估计的根 n 时。考虑两类引导方法：可交换加权引导方法 (EWB) 和基于模型的引导方法（也称为参数引导方法）。 PI 证明 EWB 一致地估计了欧几里得估计的渐近方差，并且在惩罚 M 估计框架中得出半参数推论在理论上是有效的。然而，EWB 在对非参数分量进行推断时可能会变得无效。因此，PI 考虑基于模型的引导程序，并从理论上证明它是对半非参数模型中的所有参数普遍有效的推理过程。拟议的研究还涉及先进经验过程工具的开发。上述研究为通过各种自举采样方案进行一般的半非参数推理奠定了理论基础，并建立了关于非参数分量的非标准渐近理论的通用框架。迫切需要快速有效地从所有维度中提取信息。现代海量数据集导致半非参数模型越来越受欢迎。例如，为了理解最近的金融危机，半非参数 copula 模型被用来解决不同金融序列冲击之间的尾部依赖性，并恢复单个金融序列的影响曲线的形状。拟议的研究通过开发一系列创新且有效的引导推理工具，促进半非参数模型在分析现代复杂数据中的使用，并最终在各个学科中获得可观的科学生产力。统计科学受益于越来越多的研究人员从统计和科学角度接受半非参数建模培训。这将包括这项工作资助的学生、更广泛的合作研究和教育活动。上述研究还为公众制作了易于实施的软件。