一般误差分布下若干半参数模型的复合分位数方法

项目名称： 一般误差分布下若干半参数模型的复合分位数方法

项目编号： No.11426126

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 孙静

作者单位： 鲁东大学

项目金额： 3万元

中文摘要： 半参数模型的估计问题虽然已经得到广泛的研究和应用，但是关于其稳健估计方法的研究相对较少。近年来新提出的复合分位数回归可以兼顾效率和稳健性。但是，现有的复合分位数方法需要一个基本的假设：随机误差的分布是对称的。没有这个前提条件，将出现一系列本质性问题，如估计是有偏的、不相合的。同时，现有的复合分位数回归采用最简单的等权重复合方式，没有考虑使用最优权重。针对这些问题，本项目致力于研究一般误差分布下若干半参数模型的复合分位数方法；特别地，我们将对单指标模型展开研究。主要研究内容为：一是利用复合分位数的思想给出参数部分的估计；二是摆脱误差分布对称的假设，针对非参数部分建立相合的复合分位数估计类；三是从相合估计类中确定最优的非参数估计，证明最优权重的存在唯一性并讨论其实际计算方法。由于实际中误差分布的对称性通常无法预知，因此本研究理论上有所创新，方法具有实际应用价值。

中文关键词： 稳健方法；复合分位数回归；缺失数据；经验似然；条件特征筛选

英文摘要： The estimation problem of semiparametric models has been widely studied and applied, but there's less study on its robust estimation method. Recently the new proposed composite quantile regression can take into account both efficiency and robustness. However, the existing composite quantile regression is based on the assumption of symmetric errors, without which a series of essential issues will inevitably emerge. For example, the estimates will be biased, inconsistent. Meanwhile, the existing composite quantile regression uses uniform weights, thus ignores using optimal weights. To solve these problems, this project aims to study the composite quantile method of some semiparametric models for the case of general error distributions. In particular, we will focus on the study of single-index models. The main contents are as follows: firstly, we give the estimate for the parametric part using the idea of composite quantile regression; secondly, we get rid of the assumption of symmetric errors, and construct consistent composite quantile estimates for the nonparametric part; thirdly, we search the optimal nonparametric estimate from the consistent estimate class obtained from the second step, prove the existence and uniqueness of the optimal weights, and discuss its estimation procedure in practice. Due to the unpr

英文关键词： Robust method；composite quantile regression；missing data；empirical likelihood；conditional feature screening