Simulation-based multiple inference problems: theory and application

基于仿真的多重推理问题：理论与应用

• 批准号: RGPIN-2019-06114
• 负责人: Khalaf, Lynda
• 金额: $ 1.46万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=751466
• 关键词: Simulation; based; multiple; inference; problems

Econometricians are often presented with many inference problems to consider at the same time. While related problems are not completely overlooked, recent critical reviews reveal that attention to these issues is not ubiquitous particularly in observational studies. This program considers combined simulation-based testing and inference problems, with focus on inequality analysis. Increasingly common statistical tools now involve simulation methods. With reference to the existing literature on the statistical validity of such methods, formal works on combined methods are relatively scarce. Methodologically, this proposal will also contribute to this literature. Research on inequality, including work by Nobel laureate Simon Kuznets, has a long history in the discipline. Timely questions popularized by e.g. Thomas Piketty have shaken the discipline worldwide. This proposal aims to develop and validate concrete statistical tools towards evidence-based inequality analysis, building on the fact that inequality measures are multi-dimensional, conceptually and definitionally. A wide range of such measures [e.g. the generalized entropy and Gini indexes, quantile ratios] involve nonlinear transformations of moments or quantiles. Whether estimated jointly or individually, parametrically or non-parametrically, with just one or using several variables, definitional non-linearities have non-trivial implications on the statistical properties of associated estimators and test statistics. Conflict among test criteria on inequality is also prevalent, and inference remains a challenging problem because underlying distributions have heavy tails. In this context, this research program aims to address the following questions. Is it legitimate from an error control perspective to apply existing and popular statistical methods for multi-criteria-based inference approach to inequality? Which error rate principles and combination methods will deliver reliable and policy relevant inference? Can existing validity conditions for simulation-based methods be verified or eventually extended for this purpose? I intend to propose and validate a concrete strategy for combined testing and simultaneous inference on a vector of measures, as well as a formal policy-relevant analysis on the concrete choice between combination and separation of the inference problems. Important features of the proposed methodology address nuisance parameters in locally identified and identification-robust contexts. In addition to testing, my research program will yield simultaneous confidence sets for objects of interest. Moments and quantile-based measures will differ importantly with respect to asymptotic and finite sample considerations. Distribution-free methods will be proposed for using quantiles, whereas parametric methods will embed distributional fit. As more and more measures may be combined, robustness to dimensionality will be considered.

经济学家通常会同时考虑许多推理问题。尽管没有完全忽略相关问题，但最近的批判性评论表明，对这些问题的关注并不是无处不在的，尤其是在观察性研究中。该计划认为基于模拟的测试和推理问题的合并，重点是不平等分析。现在越来越常见的统计工具涉及模拟方法。关于此类方法的统计有效性的现有文献，关于合并方法的正式作品相对较少。从方法上讲，该提议也将有助于这一文献。关于不平等的研究，包括诺贝尔奖获得者西蒙·库兹尼茨（Simon Kuznets）的工作，在该学科中有着悠久的历史。及时的问题，例如托马斯·皮凯蒂（Thomas Piketty）在全球范围内动摇了这一学科。该建议旨在开发和验证具体的统计工具来基于证据的不平等分析，这是基于以下事实：不平等措施在概念和定义上都是多维的。 多种此类措施[例如广义熵和Gini指数，分位数比]涉及矩或分位数的非线性变换。无论是共同或单独，参数或非参数估计的，仅使用一个或使用几个变量，定义性非线性都对关联估计器和测试统计量的统计属性具有非平凡的影响。关于不平等的测试标准之间的冲突也很普遍，推论仍然是一个具有挑战性的问题，因为潜在的分布有沉重的尾巴。在这种情况下，该研究计划旨在解决以下问题。从错误控制的角度来看，它是否合理地将现有和流行的统计方法应用于基于多准则的推理方法不平等？哪些错误率原则和组合方法将提供可靠且政策相关的推断？是否可以为此目的验证或最终扩展基于仿真方法的现有有效性条件？我打算提出和验证一种具体的策略，以对措施向量进行合并测试和同时推断，以及对推理问题组合和分离之间的具体选择的正式政策分析。所提出的方法的重要特征在本地识别和识别式上下文中介绍了滋扰参数。除了测试外，我的研究计划还将为感兴趣的对象提供同时的信心集。相对于渐近和有限的样本注意事项，矩和分位数的措施将有所不同。将提出无分布方法用于使用分位数，而参数方法将嵌入分布拟合。随着越来越多的措施结合在一起，将考虑对维度的鲁棒性。