单指标分位回归模型估计的MM算法

doi:10.7523/j.issn.2095-6134.2021.03.001

中国科学院大学学报 ›› 2021, Vol. 38 ›› Issue (3): 289-296.DOI: 10.7523/j.issn.2095-6134.2021.03.001

• 数学与物理学 • 下一篇

单指标分位回归模型估计的MM算法

郭媛媛¹, 杨雪梅², 孙志华^1,3

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

收稿日期:2019-05-14 修回日期:2019-10-09 发布日期:2021-05-17
通讯作者: 孙志华
基金资助:
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

MM algorithm of the estimation of single-index quantile regression

GUO Yuanyuan¹, YANG Xuemei², SUN Zhihua^1,3

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

Received:2019-05-14 Revised:2019-10-09 Published:2021-05-17

摘要/Abstract

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，再逐步迭代至收敛。数值模拟和实证研究表明MM算法在单指标分位回归模型的估计中具有较好的稳定性，能够得到比较准确的估计结果，且相比于内点法，计算效率更高，耗时更短。

关键词: 单指标分位回归模型, MM算法, 替代函数, 计算效率

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.

Key words: single-index quantile regression model, MM-algorithm, surrogate function, computational efficiency

中图分类号:

O212.4

郭媛媛, 杨雪梅, 孙志华. 单指标分位回归模型估计的MM算法[J]. 中国科学院大学学报, 2021, 38(3): 289-296.

GUO Yuanyuan, YANG Xuemei, SUN Zhihua. MM algorithm of the estimation of single-index quantile regression[J]. Journal of University of Chinese Academy of Sciences, 2021, 38(3): 289-296.

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单指标分位回归模型估计的MM算法

MM algorithm of the estimation of single-index quantile regression

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