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介绍了在半非偏射模型的背景下，针对两种广泛的引导方法的自举推断策略。作为统计推断的通用方法，Bootstrap在半非偏射模型中发现了广泛的应用。不幸的是，关于自举推断的系统理论研究极为有限，尤其是当非参数成分不可估计时。考虑了两类的引导方法：交换加权的引导程序（EWB）和基于模型的引导程序（也称为参数引导程序）。 PI证明EWB始终估算欧几里得估计值的渐近方差，并且在理论上在绘制惩罚的M估计框架中绘制半参数推断方面是有效的。但是，EWB可能无效地绘制非参数组件的推断。因此，PI考虑了基于模型的引导程序，从理论上讲，它是半非帕拍模型中所有参数的普遍有效的推理过程。拟议的研究还涉及开发先进的经验过程工具。 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.例如，为了了解最近的金融危机，半非帕拉梅特里库模型用于解决对不同财务系列的冲击之间的依赖，并恢复单个财务系列的影响曲线的形状。拟议的研究促进了通过开发一系列创新和有效的自举推断工具来分析现代复杂数据来分析现代复杂数据的使用，并最终在各个学科中获得了实质性的科学生产力。统计科学从统计和科学观点培训的培训中越来越多的研究人员受益。这将包括由这项工作资助的学生，更广泛的研究和教育活动。以上研究还为公众提供易于实施的软件。