Mathematical Sciences: Regression Quantile Methods and Asymptotic Statistical Theory

数学科学：回归分位数方法和渐近统计理论

• 批准号: 8802555
• 负责人: Stephen Portnoy
• 金额: $ 10.54万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802555&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Regression; Quantile; Methods

The research objectives involve extending the regression quantile methodology and developing new asymptotic approaches to cases of large parametric dimension. Methodological aims include the following: (a) to develop adaptive estimators in the linear regression model which are fully efficient under any assumption on the error distribution, (b) to define and investigate outlier detection prodedures and to apply them for providing resistance to the presence of outliers and influential observations, (c) to investigate the performance of the regression quantile algorithm, and (d) to obtain robust analyses for nonlinear regression models and for structural models in econometrics. Aims for new asymptotic approaches include the following: (a) to obtain appropriate asymptotic results for the regression quantile methodology in linear models, (b) to study standard and robust methods for analyzing structural models, and (c) to investigate the adequancy of such asymptotic approximations for real and simulated data sets. This research in the field of statistics is to develop and analyze robust econometric procedures. Robust statistical methods are procedures that work well even when applied to situations where the underlying assumptions in the mathematics are unrealistic and do not hold. Since mathematical models of the economy are approximations of very complex systems for which the true underlying mathematical representation may well be unknown, and since data brings measurement error and other uncertainty with its very creation, it is advantageous to have statistical techniques that are known to perform well under adverse conditions.

研究目标包括扩展回归 分位数方法和发展新的渐近方法， 大参数尺寸的情况。 方法目标包括 （a）在线性模型中建立自适应估计器 在任何假设下都是完全有效的回归模型 关于误差分布，（B）定义和研究 异常值检测程序，并应用它们提供 对离群值和有影响力的 （c）调查执行情况; 回归分位数算法，以及（d）获得稳健的分析 非线性回归模型和结构模型 计量经济学 新渐近方法的目标包括： 以下：（a）获得适当的渐近结果， 线性模型中的回归分位数方法，（B）研究 用于分析结构模型的标准和可靠方法，以及 (c)研究这种渐近的充分性 真实的和模拟数据集的近似。 统计学领域的这项研究是为了发展和 分析稳健的计量经济学程序。 稳健统计 方法是即使应用于 数学中的基本假设 是不现实的，也不成立。 因为数学模型 经济是非常复杂系统的近似， 真正的基本数学表示很可能是 未知，由于数据带来测量误差和其他 不确定性与其本身的创造，这是有利的， 已知在以下情况下表现良好的统计技术 不利条件。