高维尾期望回归模型分布式估计方法的改进  

Improvement of Distributed Estimation Method for High Dimensional Tail Expectile Regression Model

作　　者：朱霞[1] 潘莹丽 Zhu Xia;Pan Yingli(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China;School of Mathematics and Statistics,Hubei University,Wuhan 430062,China;Hubei Key Laboratory of Applied Mathematics,Hubei University,Wuhan 430062,China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]湖北大学数学与统计学学院,武汉430062 [3]湖北大学应用数学湖北省重点实验室,武汉430062

出　　处：《统计与决策》2023年第18期33-38,共6页Statistics & Decision

基　　金：科技大数据湖北省重点实验室开放基金资助项目(KF2022002)。

摘　　要：文章针对高维尾期望回归模型的估计问题提出了一种在交互有效的替代损失(CSL)方法基础上进行优化函数改进的分布式估计方法,具体的改进步骤为:通过构建正则化的梯度增强型损失(GEL)函数,使所有Worker机器都能并行地优化各自对应的正则化GEL函数,并通过Master机器对计算结果进行更新。数值模拟和实证分析验证了该改进方法的估计误差收敛于基于所有数据的Centralize方法的估计误差,且相对于CSL方法,该方法具有较快的收敛速度。Aiming at the estimation problem of high-dimensional tail expectile regression,this paper proposes a distributed estimation method with improved optimization function on the basis of communication-efficient surrogate loss(CSL)method.The specific improvement steps are as following:By constructing regularized gradient-enhanced loss(GEL)functions,all Worker machines are enabled to optimize their corresponding regularized GEL functions in parallel,and the calculation results are updated through Master machines.Numerical simulation and empirical analysis verify that the estimation error of the improved method converges to that of the Centralize method based on full data,and that the proposed method has a faster convergence rate than the CSL method.

关 键 词：尾期望 分布式改进估计 正则化 GEL函数 

分 类 号：O212[理学—概率论与数理统计]