Robust Frontier and Boundary Estimation: Theory and Application

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。本研究项目旨在利用有效的多项式样条分位数平滑方法开发各种非参数和半参数前沿模型的鲁棒估计方法。更具体地说，提出的研究目标包括：为非参数和半参数前沿模型提出一种易于使用的鲁棒估计方法；开发一种创新的惩罚多项式样条分位数回归，用于非参数和半参数前沿模型的变量选择和有效估计；研究所提方法的渐近性质并开发有效的数值算法。P.I.还计划研究柔性半参数ARCH模型的多项式样条估计，并制定基于多项式样条估计的非参数似然比检验，以推断半参数ARCH模型中的系数函数。本研究为曲线拟合提供了新的方法和理论。所提出的研究结果对广泛领域的研究人员非常有用。例如，它可以增强对宏观经济变量对股票价格影响的理解，有利于投资银行改善风险管理。此外，建议的研究将通过开发非参数方法和时间序列分析的研究生课程纳入教学活动，这将促进学生参与当前科学的研究。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This research project aims to develop robust estimation methods for various non- and semiparametric frontier models using the efficient polynomial spline quantile smoothing method. More specifically, the objectives of the proposed research include: to propose an easy-to-use robust estimation procedure for non- and semi-parametric frontier models; to develop an innovative penalized polynomial spline quantile regression for variable selection and efficient estimation of non- and semi-parametric frontier models; to study the asymptotic properties and develop efficient numerical algorithms of the proposed methods. The P.I. also plans to investigate polynomial spline estimations of flexible semiparametric ARCH models and formulate a nonparametric likelihood ratio test based on polynomial spline estimation to make inferences of the coefficient functions in the semiparametric ARCH model.The proposed research generates new methods and theories of curve fitting. The results of the proposed research are very useful for researchers in a wide range of fields. For example, it can be used to enhance the understanding of the impact of the macro economic variables on the stock prices and benefit investment banks to help improve risk management. Furthermore, the proposed research will be incorporated into teaching activities through development of a graduate course on nonparametric methods and time series analysis, which promotes involvement of students in the research of current sciences.