海量数据下光滑分位数回归聚合估计  

Aggregate Estimation of Smoothing Quantile Regression Under Massive Data

作　　者：聂浩巍 李志强 Nie Haowei;Li Zhiqiang(College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,China)

机构地区：[1]北京化工大学数理学院,北京100029

出　　处：《统计与决策》2023年第21期34-39,共6页Statistics & Decision

摘　　要：计算机内存限制和分位数回归损失函数的不光滑性,对海量数据下分位数回归的研究提出了挑战。文章将聚合估计方程与核卷积光滑方法相结合,提出了一种在分布式环境下基于估计方程的光滑分位数的回归聚合估计算法(DSCQR)。理论研究表明,在分块数K满足一定条件时,聚合估计量与全样本估计量具有相同的渐近性质。模拟和实证研究结果表明,所提方法和已有研究提出的DCQR方法相比,在计算速度上具有显著优越性,且在K满足一定条件时具有相当的稳健性。Computer memory limitations and the non-smoothness of quantile regression loss function pose challenges to the research of quantile regression under massive data.This paper combines the aggregation estimation equation with the convolu-tion-based kernel smoothing method and proposes an aggregate estimation algorithm of smoothing quantile regression based on es-timation equations in a distributed environment(DSCQR).Theoretical research shows that when the block number K satisfies cer-tain conditions,the aggregate estimator and the full sample estimator have the same asymptotic properties.The simulation and em-pirical study results demonstrate that the proposed method has obvious advantages in computation speed compared with the DCQR method proposed in previous studies,and also has considerable robustness when K meets certain conditions.

关 键 词：分位数回归 海量数据 核卷积光滑 分治算法 

分 类 号：O212.7[理学—概率论与数理统计]