最小一乘导数估计的统计方法与优化  

Statistical Methods and Optimization of Least Absolute Derivative Estimation

作　　者：支席年 夏小娜 Zhi Xinian;Xia Xiaona(School of Statistics,Qufu Normal University,Rizhao Shandong 276826,China;Chinese Academy of Education Big Data,Qufu Normal University,Qufu Shandong 273165,China;School of Information Science and Engineering,Qufu Normal University,Rizhao Shandong 276826,China)

机构地区：[1]曲阜师范大学统计学院,山东曲阜273165 [2]曲阜师范大学中国教育大数据研究院,山东曲阜273165 [3]曲阜师范大学信息科学与工程学院,山东日照276826

出　　处：《统计与决策》2021年第13期32-36,共5页Statistics & Decision

基　　金：山东省教育科学“十三五”规划重点课题(2020ZD030)。

摘　　要：对于非正态数据,基于最小二乘的导数估计方法不能保证估计效率,甚至会得到错误的结论。局部加权最小一乘回归方法解决了非正态分布样本中估计效率低和稳健性差的问题。文章以中国、美国、日本和南非4个国家1959—2017年的总人口数据和人均GDP数据为样本,将环比增长率和基于局部加权最小绝对偏差回归导数估计的结果进行比较,通过设计对应的可执行算法,展开验证与分析。结果表明:相比于环比增长率,该方法对于具有时间序列特征的数据处理具有通用性,可以准确地得到其回归模型在每一点的导数值,灵敏地反映出数据的变化趋势,有利于同类大数据的研究分析和决策学习。For non-normal data, the derivative estimation method based on least squares cannot guarantee the estimation efficiency, and may even get wrong conclusions;locally weighted least absolute regression method solves the problem of low estimation efficiency and poor robustness in non-normal distribution samples. This paper takes the data of total population and per capita GDP of China, the United States, Japan and South Africa from 1959 to 2017 as samples to compare the quarter-on-quarter growth rate with the results based on the locally weighted least absolute deviation regression derivative estimation, and then conducts verification and analysis through designing the corresponding executable algorithm. The results show that, compared with quarter-on-quarter growth rate, this method has universality for data processing with time series characteristics, and can accurately obtain the derivative value of the regression model at each point, sensitively reflecting the change trend of the data, conducive to the analysis of similar big data and decision-making learning.

关 键 词：数据挖掘 非参数统计 导数估计 最小一乘回归方法 时间序列 

分 类 号：F224.7[经济管理—国民经济]