Regression Quantiles and Global Measures of Robustness

经济学家一直在寻找更稳健的统计技术，这样偏离标准假设就不会扰乱估计过程。回归分位数方法以及“分解”和“尾部行为”测量，是本研究项目的重点，对于开发更健壮的替代方法具有很大的希望。该项目关于回归分位数的具体目标是改进目前的方法，并开发用户友好的算法和程序，以便将这些方法应用于线性模型和相关领域，进一步扩展理论以包括相关和非平稳情况，研究对偶回归分位数及其相应的秩统计量，并在有大量参数的情况下开发大维渐近性。第二条研究路线涉及全球稳健性测量及其与离群值诊断的关系。将完成分析，以便更全面地了解是什么导致统计程序在存在异常值的情况下崩溃，特别是通过探索有限样本“崩溃”和估计者的“尾部行为”之间的密切联系，改进目前检测和调整异常值的程序，并开发高度抵抗异常值和有影响的观测的推断方法。该项目创建的算法的开发和分发将加速应用研究人员在经济学中使用这些重要的方法论发展。扩展理论工作最终将带来更好的实证工作，因为偏离基本假设，如正态和独立性，将不再必然导致模拟技术的崩溃。

Economists are constantly in search of more robust statistical techniques so that departures from standard assumptions will not disrupt the estimation process. Regression quantile methods and "breakdown" and "tail-behavior" measures, the foci of this research project, hold a great deal of promise for developing more robust alternatives. The specific objectives of the project with respect to regression quantiles are to refine the current methods and to develop user friendly algorithms and programs for applying these methods in linear models and related areas, further extending the theory to include dependent and non-stationary cases, to study dual regression quantiles and their corresponding rank statistics and to develop large dimension asymptotics where there are a large number of parameters. A second line of research involves global measures of robustness and their relation to outlier diagnostics. Analyses will be completed to understand more completely what causes statistical procedures to break down in the presence of outliers, particularly through the exploration of the close connection between finite-sample "breakdown" and "tail behavior" of estimators, and to refine current procedures for detecting and adjusting for outliers and to develop inference methods that are highly resistant to the presence of outliers and influential observations. The development and distribution of the algorithms created by this project will hasten the use of these important methodological developments by applied researchers in economics. Extending the theoretical work will eventually result in better empirical work, as the departures from underlying assumptions like normality and independence will no longer necessarily lead to a breakdown in esimtation techniques.