两种概率密度导数估计方法的比较研究  

A comparison of two estimation methods for probability density’s derivatives

作　　者：王文武 孔德茹 WANG Wenwu;KONG Deru(School of Statistics and Data Science,Qufu Normal University,273165,Qufu,Shandong,PRC)

机构地区：[1]曲阜师范大学统计与数据科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2022年第4期14-21,共8页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(12071248);国家统计局全国统计科学重点项目(2020LZ26)。

摘　　要：概率密度函数导数的估计存在两种流行方法——核方法和局部多项式回归方法.该文从理论和模拟两个方面比较这两种方法.首先,在理论上总结两种估计的渐近性质;其次,对均匀分布、正态分布、卡方分布的概率密度导数进行数值模拟,比较两种方法在3种分布下的经验均方误差和其他统计性质.结果表明:相较于核方法,局部多项式回归方法在估计概率密度导数时一般更具有稳健性和边界自适应性等优势.There are two methods of estimating probability density’s derivative,kernel method and local polynomial regression method.In this paper,the two methods by theory comparison and simulation study are discussed.Firstly,the asymptotic properties of the two estimators are summarized.Secondly,simulation for comparing the two methods is conducted,in which the error distributions are uniform distribution,normal distribution and chi-square distribution.In addition,the empirical mean square error and other properties of these estimators are compared.The results show that in general,compared with kernel method,local polynomial regression method has the advantages of robustness and boundary adaptability when estimating the derivative of probability density.

关 键 词：概率密度导数 局部多项式回归方法 核方法 数值模拟 

分 类 号：O211[理学—概率论与数理统计]