General Semiparametric Inference via Bootstrap Sampling

通过 Bootstrap 采样进行一般半参数推理

• 批准号: 0906497
• 负责人: Guang Cheng
• 金额: $ 10万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906497&HistoricalAwards=false
• 关键词: General; Semiparametric; Inference; via; Bootstrap

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The research objectives of this project are first to prove the theoretical validity of the bootstrap method as a general inferential tool for the semiparametric models, and then invent a computationally attractive bootstrap inference procedure, called k-step bootstrap. Semiparametric modelling has provided an excellent framework for the modern complex data due to its flexibility to model some features of the data parametrically but without assuming anything for the other features. The bootstrap is the most popular data-resampling method used in statistical analysis, and has recently been applied to the semiparametric models arising from a wide variety of contexts. Therefore, the systematic theoretical studies on the bootstrap inferences for the semiparametric models are fundamentally important. In practice, the computational cost of the bootstrap inference procedure is particularly high for the semiparametric models. Thus, the investigator proposes an approximate bootstrap method, i.e. k-step bootstrap, and will show that this novel approach results in huge computational savings but without sacrificing any degree of inference accuracy. In addition, the investigator will develop a set of asymptotic results to elucidate the asymptotic structure of the semiparametric M-estimation, which is crucial for the future theoretical research. M-estimation refers to a general method of estimation including the maximum likelihood estimation as a special case.The primary impact of the proposed work is to lay solid theoretical foundation for the general semiparametric inferences via bootstrap sampling. In addition, the proposed k-step bootstrap approach is practically beneficial in several regards. For instance, the scientists who bootstrap a large data set will benefit, as the minimal computational cost needed in the k-step bootstrap to achieve the satisfactory inference accuracy will be precisely analyzed. However, the broader impacts of the proposed activities are multiple. For instance, a key aspect of this project is the integration of research and teaching, which will be achieved by proposing specific projects for students during the teaching of classes on semiparametric inferences and bootstrap computation. This pedagogical method also facilitates the participation of underrepresented groups of students.

该奖项根据 2009 年《美国复苏和再投资法案》（公法 111-5）提供资金。该项目的研究目标首先是证明引导方法作为半参数模型的通用推理工具的理论有效性，然后发明一种计算上有吸引力的引导推理程序，称为k步引导。 半参数建模为现代复杂数据提供了一个优秀的框架，因为它可以灵活地对数据的某些特征进行参数化建模，但无需对其他特征进行任何假设。引导程序是统计分析中最流行的数据重采样方法，最近已应用于各种背景下产生的半参数模型。因此，对半参数模型的引导推理进行系统的理论研究具有十分重要的意义。实际上，对于半参数模型，引导推理过程的计算成本特别高。因此，研究人员提出了一种近似引导方法，即 k 步引导方法，并将表明这种新颖的方法可以节省大量计算量，但不会牺牲任何程度的推理准确性。此外，研究者将开发一组渐近结果来阐明半参数M估计的渐近结构，这对于未来的理论研究至关重要。 M估计是指一种通用的估计方法，包括作为特殊情况的最大似然估计。所提出的工作的主要影响是为通过引导抽样的一般半参数推理奠定坚实的理论基础。此外，所提出的 k 步引导方法在多个方面实际上都是有益的。例如，引导大型数据集的科学家将受益，因为将精确分析 k 步引导中实现令人满意的推理精度所需的最小计算成本。然而，拟议活动的更广泛影响是多重的。例如，该项目的一个关键方面是研究与教学的结合，这将通过在半参数推理和引导计算课程的教学中为学生提出具体的项目来实现。这种教学方法还促进了代表性不足的学生群体的参与。