Simulation-based multiple inference problems: theory and application

计量经济学家经常同时面临许多需要考虑的推理问题。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。这个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涉及模拟方法。从已有的关于这两种方法统计有效性的文献来看，关于组合方法的正式研究相对较少。在方法上，本建议也将有助于本文献。对不平等的研究，包括诺贝尔奖得主西蒙·库兹涅茨（Simon Kuznets）的研究，在该学科中有着悠久的历史。托马斯·皮凯蒂（Thomas Piketty）等人提出的及时问题在全世界范围内动摇了这门学科。基于不平等衡量是多维的、概念上的和定义上的这一事实，本提案旨在开发和验证以证据为基础的不平等分析的具体统计工具。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，参数化还是非参数化估计，仅使用一个变量还是使用几个变量，定义非线性对相关估计量和检验统计量的统计性质具有重要的含义。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有很重的尾巴，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标准的推理方法来处理不等式是否合理？哪些错误率原则和组合方法将提供可靠且与策略相关的推断？是否可以为此目的验证或最终扩展基于仿真的方法的现有有效性条件？我打算提出并验证在度量向量上进行组合测试和同时推理的具体策略，以及对推理问题的组合和分离的具体选择进行正式的与政策相关的分析。提出的方法的重要特点是在局部识别和识别鲁棒性上下文中解决了干扰参数。除了测试之外，我的研究计划还将为感兴趣的对象同时生成置信度集。矩和基于分位数的测量将在渐近和有限样本考虑方面有重要的不同。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。随着越来越多的测度可以组合在一起，对维度的鲁棒性将被考虑。

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.