Inference on Extremes in Economic Regression Analysis

该项目的目的是大幅度改变经济回归分析中研究极端现象的方法和软件。更具体地说，该项目为极值分位数回归开发了可行和实用的推理方法-描述回归量X如何影响尾部兴趣Y的结果的模型。例如，极值分位数回归描述了母亲的社会经济特征（吸烟、保健、教育）如何影响出生体重的极低分位数。该项目使对这种回归关系进行推断成为可能。该项目开发参数和非参数极值分位数回归模型的推理方法，以及实现这些方法的公共软件（基于免费软件环境）。该项目严格关注以下三个部分：(1)线性极值分位数回归的推理方法，(2)非参数极值分位数回归的推理方法，(3)实现(1)和(2)的软件包（免费和公开可用）。该软件将作为文档化的r包提供，其中包含帮助文件和小说明。该文档将包含对这些方法的简短描述，然后是使用有趣数据集的教程示例。提案的广泛影响：如上所述，该项目的目的之一是生产实现极值分位数回归推理方法的公共软件。软件包可用后，任何从业者都可以从r网站www.r-project.org下载并安装该软件包，并在帮助文件和教程示例的帮助下，将其用于分析任何数据集。应该提到的是，选择R作为编程环境的原因是，它作为研究人员（计量经济学家、统计学家、生物计量学家）和从业者广泛使用的通用、免费的统计环境。这是拟议项目的更广泛影响的特点。该项目还将通过两名学生的帮助产生直接的教育影响：一名本科生和一名研究生。研究生将是共同作者，两名学生将是软件包的共同作者和共同开发者。

The purpose of the project is to change dramatically the methods and software available for studying extreme phenomena in economic regression analysis. More specifically, the project develops feasible and practical inference methods for extremal quantile regressions - the models that describe how regressors X affect the outcome of interest Y in the tails. For example, extremal quantile regressions describe how mothers' socio-economic characteristics (smoking, health-care, education) affect the very low quantiles of birthweights. The project makes it possible to make inferences about such regression relationships. The project develops inference methods for parametric and non-parametric extremal quantile regression models and public software (based on the freeware environment) that implements these methods. The project is strictly focused on the following three parts:(1) Inference methods in linear extremal quantile regression,(2) Inference methods in nonparametric extremal quantile regression,(3) Software package (free and publicly available) which implements (1) and (2). The software will be available as a documented R-package with help files and a vignette. The vignette is the document that will contain a short description of the methods, followed by tutorial examples using interesting data sets.Broader Impact of the Proposal: As stated above, one of the purposes of the project is to produce public software that implements inference methods for extremal quantile regression. After the software package is available, any practitioner will be able to download and install the package from R-website www.r-project.org and use it in the analysis of any data-set, aided by help files and tutorial examples. It should be mentioned that the reason for choosing R as a programming environment is that it serves as a common, free statistical environment widely used by researchers (econometricians, statisticians, biometricians) and practitioners. This characterizes the broader impact of the proposed project. The project will also have direct educational impact by involving help of two students: one undergraduate student and one graduate student. The graduate student will be a coauthor, and both students will be co-authors and co-developers of the software package.