Simulation-based multiple inference problems: theory and application

计量经济学家经常同时面临许多推理问题。虽然相关的问题并没有完全被忽视，但最近的评论表明，对这些问题的关注并不普遍，特别是在观察性研究中。该程序考虑了基于模拟的测试和推理问题，重点是不等式分析。现在越来越常见的统计工具包括模拟方法。参考现有的文献，这些方法的统计有效性，正式的工作相结合的方法是相对稀缺的。在方法上，这一建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（Simon Kuznets）的工作，在该学科中有着悠久的历史。由托马斯皮凯蒂（Thomas Piketty）等人提出的及时性问题已经在全世界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，以便进行循证的不平等分析，同时考虑到不平等措施是多层面的，在概念上和定义上都是如此。 许多这样的度量[例如广义熵和基尼指数、分位数比率]涉及矩或分位数的非线性变换。无论是联合或单独估计，参数或非参数，只有一个或使用几个变量，定义的非线性相关的估计量和检验统计量的统计特性有非平凡的影响。关于不平等的检验标准之间的冲突也很普遍，而且由于潜在的分布具有厚尾，因此推断仍然是一个具有挑战性的问题。在此背景下，本研究计划旨在解决以下问题。从误差控制的角度来看，将现有的和流行的统计方法应用于基于多准则的推理方法来处理不平等问题是否合法？哪些错误率原则和组合方法将提供可靠的和政策相关的推断？基于模拟的方法的现有有效性条件是否可以验证或最终扩展？我打算提出并验证一个具体的策略，结合测试和同时推理向量的措施，以及正式的政策相关的分析，具体的选择之间的组合和分离的推理问题。所提出的方法的重要功能解决滋扰参数在本地识别和识别鲁棒性的上下文中。除了测试之外，我的研究计划还将为感兴趣的对象产生同步置信集。矩和分位数为基础的措施将有很大的不同方面的渐近和有限样本的考虑。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。随着越来越多的测量可以被组合，将考虑对维度的鲁棒性。

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.