| 单指标分位回归模型估计的MM算法 |
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| 作者姓名： | 郭媛媛 杨雪梅 孙志华 |
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| 作者单位： | 1. 中国科学院大学数学科学学院, 北京 100049;2. 华北电力大学数理学院, 北京 102206;3. 中国科学院大数据挖掘与知识管理重点实验室, 北京 100190 |
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| 基金项目： | 国家自然科学基金（11971045）、中央高校基本科研业务费专项资金和中国科学院大数据挖掘与知识管理重点实验室开放课题资助 |
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| 摘 要： | 单指标分位回归模型是一类重要的半参数模型,具有降维的优点的同时保留了非参数分位回归模型的稳健性.但现有的单指标分位回归模型的估计程序大部分都是通过内点法来实现.对单指标分位回归模型估计程序的MM (majorize-minimize)算法进行研究.首先找到目标函数的优化函数,然后通过最小化优化函数来得到估计,再逐步迭代...
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| 关 键 词： | 单指标分位回归模型 MM算法 替代函数 计算效率 |
| 收稿时间： | 2019-05-14 |
| 修稿时间： | 2019-10-09 |
MM algorithm of the estimation of single-index quantile regression |
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| Authors: | GUO Yuanyuan YANG Xuemei SUN Zhihua |
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| Institution: | 1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;3. Key Laboratory of Big Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | The single-index quantile regression model is an important semiparametric model with the merit of dimensionality reduction. Furthermore, it retains the robustness of a nonparametric model. For most existing estimating procedures of single-index quantile regression models, the estimators are obtained via minimizing the objective functions by the interior point method. In this paper, we investigate the MM (majorize-minimize) algorithm of the single index quantile regression model estimating procedure. We first construct the majorize function of the objective function and then minimize the substituted majorize function to find the estimators. Our numerical simulations and empirical study show that for the considered model, the MM algorithm has good stability and can yield more accurate estimation. Compared with the interior point method, the MM algorithm is more efficient and takes less time. |
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| Keywords: | single-index quantile regression model MM-algorithm surrogate function computational efficiency |
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