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.

该奖项是根据2009年《美国复苏与再投资法》（公法111-5）资助的。该项目的研究目标首先证明了Bootstrap方法的理论有效性，作为半参数模型的一般推论工具，然后发明了一种计算上有吸引力的Bootstrap推理程序，称为K-Step Bootstrap。 半参数建模为现代复杂数据提供了出色的框架，因为它的灵活性可以在参数上对数据的某些特征进行建模，但没有为其他功能假设任何东西。 Bootstrap是统计分析中使用的最流行的数据换采样方法，最近已应用于由多种环境引起的半参数模型。因此，关于半摩托模型的自举推断的系统理论研究在根本上很重要。在实践中，对于半参数模型而言，引导性推理过程的计算成本尤其高。因此，研究者提出了一种近似的引导方法，即k-step bootstrap，并将表明这种新颖的方法可带来巨大的计算节省，但没有牺牲任何推论准确性。此外，研究者将开发一组渐近结果，以阐明半参数M估计的渐近结构，这对于未来的理论研究至关重要。 M估计是指一般的估计方法，包括最大似然估计作为一种特殊情况。拟议工作的主要影响是通过自举抽样为一般半疗法推论奠定坚实的理论基础。此外，拟议的K-Step引导方法实际上在几个方面是有益的。例如，引导大型数据集的科学家将受益，因为将精确分析K-Step Bootstrap中所需的最低计算成本，以实现令人满意的推论精度。但是，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和教学的整合，这将通过在半疗法推断和自举计算的课程中为学生提出特定项目来实现。这种教学方法还促进了代表性不足的学生的参与。