Accurate inference in high-dimensional econometrics

近几十年来，由于有了更大的数据集，研究人员开始采用所谓的“高维”模型，即包含大量变量和参数的模型。这使得在实证经济研究中调查个人决策的潜在决定因素时，可以考虑更多的个人和环境特征。然而，具有大量参数的计量经济模型具有特定的统计特性。由于这个原因，最近有大量的文献集中在高维环境中建立统计程序。虽然计量经济学中估计高维模型的方法最近已经建立，但在这些情况下如何进行统计推断仍然是很大程度上未知的。我提出的研究旨在建立这类模型的统计检验方法。更具体地说，我打算为实证经济研究的主力——线性回归模型——推导出一种适用于高维环境的稳健推理程序的概括。此外，我还打算在我的硕士论文的基础上，为高维非线性面板数据模型的统计推断方法的性质提供额外的证据。我提出的研究将有助于理论计量经济学领域的发展，并将为实证经济研究中越来越多的可用数据的分析提供重要的方法贡献。

In recent decades, the availability of larger datasets has led researchers to employ so-called "high-dimensional" models, that is models that include a large number of variables and parameters. This allows to account for a much bigger set of individual and environmental characteristics when investigating the underlying determinants of individual decisions in empirical economic research. However, econometric models with a high number of parameters feature specific statistical properties. For this reason, a large body of literature has recently focused on establishing statistical procedures in high-dimensional settings. While methods to estimate high-dimensional models in econometrics have been recently established, it remains largely unknown how statistical inference should be carried out in these settings. My proposed research aims at establishing methods for statistical testing in this type of models. More specifically, I intend to derive a generalisation of robust inference procedures to high-dimensional settings for the workhorse of empirical economic research, the linear regression model. Moreover, I also intend to build on my MSc dissertation to provide additional evidence on the properties of statistical inference methods for high-dimensional nonlinear panel data models.My proposed research would contribute to a growing field in theoretical econometrics, and would provide an important methodological contribution to the analysis of the increasing amount of available data in empirical economic research.