Simulation-based multiple inference problems: theory and application

计量经济学家经常面临许多要同时考虑的推理问题。虽然相关问题并没有被完全忽视，但最近的批评性评论表明，对这些问题的关注并不普遍，特别是在观察性研究中。该程序考虑基于模拟的测试和推理的组合问题，重点放在不等性分析上。 现在越来越常见的统计工具涉及模拟方法。就现有文献而言，关于组合方法的统计有效性的研究相对较少。在方法论上，这一提议也将有助于这一文献。 对不平等的研究，包括诺贝尔奖获得者西蒙·库兹涅茨的工作，在这一学科中有着悠久的历史。托马斯·皮凯蒂等人提出的及时问题动摇了世界范围内的这一学科。这项提议旨在开发和验证具体的统计工具，以便进行基于证据的不平等分析，其基础是不平等衡量在概念上和定义上都是多层面的。 这类度量的范围很广[例如广义熵和基尼指数、分位数比]，涉及矩或分位数的非线性变换。无论是联合估计还是单独估计，参数估计还是非参数估计，只用一个变量还是使用几个变量，定义的非线性都会对相关估计量和检验统计量的统计性质产生很大影响。关于不平等的测试标准之间的冲突也很普遍，推断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。 在此背景下，本研究计划旨在解决以下问题。从差错控制的角度来看，将现有和流行的统计方法应用于基于多标准的推理方法来处理不平等是否合法？哪些错误率原则和组合方法将提供可靠且与政策相关的推断？基于模拟的方法的现有有效性条件是否可以为此目的进行验证或最终扩展？ 我打算提出并验证对措施向量进行组合测试和同时推理的具体战略，以及对推理问题的组合和分离之间的具体选择进行正式的政策相关分析。拟议方法的重要特点是在当地确定的和识别稳健的情况下处理滋扰参数。除了测试，我的研究计划还将为感兴趣的对象产生同时的置信集。矩和基于分位数的度量在渐近和有限样本考虑方面将有很大的不同。将提出使用分位数的无分布方法，而参数方法将嵌入分布拟合。由于可以组合越来越多的度量，因此将考虑对维度的稳健性。

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.