Numerical Bootstrap and Constrained Estimation

数值引导和约束估计

• 批准号: 1658950
• 负责人: Han Hong
• 金额: $ 17.43万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1658950&HistoricalAwards=false
• 关键词: Numerical; Bootstrap; Constrained; Estimation

Many economic models used for policy evaluation are highly nonlinear, and are typically subject to nonlinear constraints on the parameters. The computational challenge in estimating these models has posed a significant obstacle for utilizing these models in effective policy making. This project assists in economic policy making by developing a new method of statistical inference that can be used to provide valid evaluation of the statistical uncertainty associated with policy-related functions of estimated parameters of economic models. This new method combines one-sided numerical differentiation with bootstrap resampling techniques to allow for non-differentiability in the policy function, and is both computationally simple and easy to implement. It can be applied to analyze oligopolistic competition in industrial organization, the effect of education policy such as the impact of smaller class sizes, and many other areas of applied economic analysis. These tools contribute to the welfare of the society by enabling models to evaluate the effectiveness of economic policies. This project studies a numerical Delta method for inference on a directionally differentiable function of regular parameters. This method is computationally efficient, does not require analytic knowledge of the structure of the function of interest, and provides uniformly valid inference for testing a one-sided hypothesis of a convex function of the parameters. In situations where the first order Delta method limiting distribution is degenerate, the second (or higher) order Delta method may provide the necessary nondegenerate large sample approximation. The investigator further generalizes the numerical Delta method to a new resampling technique called the numerical bootstrap that can consistently estimate the limit distribution in many cases -- where the conventional bootstrap is not valid and subsampling has been the most commonly used inference approach, and where the parameters are not known to be directionally differentiable. Applications include constrained and unconstrained M-estimators converging at both regular and nonstandard rates such as the maximum score model, partially identified models, misspecified simulated GMM models, and many sample size dependent statistics.

许多用于政策评估的经济模型都是高度非线性的，并且通常受到参数的非线性约束。估计这些模型的计算挑战对在有效的政策制定中利用这些模型构成了重大障碍。该项目通过开发一种新的统计推断方法来协助经济政策制定，该方法可用于对与经济模型估计参数的政策相关函数相关的统计不确定性进行有效评估。这种新方法将单侧数值微分与自举重采样技术相结合，以实现策略函数的不可微性，并且计算简单且易于实现。它可用于分析产业组织中的寡头垄断竞争、教育政策的效果（例如小班规模的影响）以及许多其他应用经济分析领域。这些工具通过启用模型来评估经济政策的有效性，从而为社会福利做出贡献。该项目研究一种数值 Delta 方法，用于推断常规参数的方向可微函数。该方法计算效率高，不需要感兴趣函数结构的分析知识，并且为检验参数凸函数的片面假设提供一致有效的推论。在一阶 Delta 方法限制分布是简并的情况下，二阶（或更高）阶 Delta 方法可以提供必要的非简并大样本近似。研究人员进一步将数值 Delta 方法推广为一种称为数值引导法的新重采样技术，该技术可以在许多情况下一致地估计极限分布 - 在传统引导法无效且子采样一直是最常用的推理方法的情况下，并且未知参数是方向可微的。应用包括以常规和非标准速率收敛的受约束和无约束 M 估计量，例如最大得分模型、部分识别模型、错误指定的模拟 GMM 模型以及许多依赖于样本大小的统计数据。

项目成果

Constrained estimation using penalization and MCMC

使用惩罚和 MCMC 进行约束估计

• DOI: 10.1016/j.jeconom.2021.02.004
• 发表时间: 2021
• 期刊: Journal of Econometrics
• 影响因子: 6.3
• 作者: Gallant, A. Ronald;Hong, Han;Leung, Michael P.;Li, Jessie
• 通讯作者: Li, Jessie

The numerical bootstrap

数值引导程序

• DOI: 10.1214/19-aos1812
• 发表时间: 2020
• 期刊: The Annals of Statistics
• 作者: Hong, Han;Li, Jessie
• 通讯作者: Li, Jessie