一元Laplace分布的L<sub>1</sub>-范估计的无偏性

王振杰; 欧吉坤; 曲国庆

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一元Laplace分布的L₁-范估计的无偏性

王振杰, 欧吉坤, 曲国庆

文章导航 > 武汉大学学报 ● 信息科学版 > 2001 > 26(4): 361-363

王振杰, 欧吉坤, 曲国庆. 一元Laplace分布的L1-范估计的无偏性[J]. 武汉大学学报 ● 信息科学版, 2001, 26(4): 361-363.

引用本文:

王振杰, 欧吉坤, 曲国庆. 一元Laplace分布的L₁-范估计的无偏性[J]. 武汉大学学报 ● 信息科学版, 2001, 26(4): 361-363.

WANG Zhenjie, OU Jikun, QU Guoqing. The Unbiasedness of L1 Estimation of Monistic Laplace Distribution[J]. Geomatics and Information Science of Wuhan University, 2001, 26(4): 361-363.

Citation:

WANG Zhenjie, OU Jikun, QU Guoqing. The Unbiasedness of L₁ Estimation of Monistic Laplace Distribution[J]. Geomatics and Information Science of Wuhan University, 2001, 26(4): 361-363.

一元Laplace分布的L₁-范估计的无偏性

1 中国科学院测量与地球物理研究所, 武汉市徐东路174号, 430077;
2 淄博学院建筑工程系, 山东省淄博市新村西路西首, 255000

基金项目: 国家自然科学基金资助项目(40074003)

详细信息

作者简介:
王振杰,讲师,博士生。现主要从事测量数据处理及其应用的研究。代表成果:抗差估计的初值选择。E-mail:zjw@sina.com

中图分类号: P207.2

The Unbiasedness of L₁ Estimation of Monistic Laplace Distribution

1 Institute of Geodesy and Geophysics, Chinese Academy of Sciences, 174 Xudong Road, Wuhan, China, 430077;
2 Department of Architecture Engineering, Zibo Institute, the West of Xincunxi Road, Zibo, China, 255000

摘要: 根据Laplace分布的概率密度函数公式,推导了中位数的概率密度,在此基础上证明了L₁-范估计的无偏性
- 中位数 /
- 无偏性 /
- 概率密度
Abstract: L₁ estimation is often used to process surveying data containing gross errors or abnormal values,it is a method of robust estimation.It is proved that L₁ estimation can resist disturbances of gross errors and its parameter MLE value is median of observed values. To the problem of unbiasedness of L₁ estimation,basing on uniqueness of solution,Zhou Shijiang proved it according to dual theorem of linear programming; and Wang Zhizhong proved it according to probability statistics theorem by using the method from special to general; also,basing on error distribution theorem and probability statistics theorem,the authors proved it.First,we deprived probability density of median closely according to probability density formula of Laplace distribution,from general to special; then we proved the unbiasedness of L₁ estimation according to probability density of median. When n is odd number,our reasoning thoughts are:(1) we rearrange observed values,big or small. (2) we deprive probability density of subsample according to probability density function of Laplace distribution. (3) we deprive probability density of median according to probability density of subsample. (4) we proved the unbiasedness of L₁ estimation according to probability density of median. Finally,we draw the conclusions:(1) L₁ estimation is unbiased estimation,and this conclusion shows L₁ estimation has good statistical characteristic. (2) the conclusion drawn by this method is same as that deprived from dual theorem of linear programming in reference ^[2],but,this conclusion is deprived from probability statistical theorem,it is simple and accepted easily. (3) this reasoning method can enlighten us to prove the unbiasedness of L_p estimation.
- median /
- unbiasedness /
- probability density

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一元Laplace分布的L₁-范估计的无偏性

1 中国科学院测量与地球物理研究所, 武汉市徐东路174号, 430077;

2 淄博学院建筑工程系, 山东省淄博市新村西路西首, 255000

基金项目: 国家自然科学基金资助项目(40074003)

作者简介:
王振杰,讲师,博士生。现主要从事测量数据处理及其应用的研究。代表成果:抗差估计的初值选择。E-mail:zjw@sina.com

收稿日期: 2001-03-21
刊出日期: 2001-04-05

中图分类号: P207.2

关键词:

中位数 /

无偏性 /

概率密度

摘要: 根据Laplace分布的概率密度函数公式,推导了中位数的概率密度,在此基础上证明了L₁-范估计的无偏性

English Abstract

The Unbiasedness of L₁ Estimation of Monistic Laplace Distribution

1 Institute of Geodesy and Geophysics, Chinese Academy of Sciences, 174 Xudong Road, Wuhan, China, 430077;

2 Department of Architecture Engineering, Zibo Institute, the West of Xincunxi Road, Zibo, China, 255000

Received Date: 2001-03-21
Publish Date: 2001-04-05

Keywords:

Abstract: L₁ estimation is often used to process surveying data containing gross errors or abnormal values,it is a method of robust estimation.It is proved that L₁ estimation can resist disturbances of gross errors and its parameter MLE value is median of observed values. To the problem of unbiasedness of L₁ estimation,basing on uniqueness of solution,Zhou Shijiang proved it according to dual theorem of linear programming; and Wang Zhizhong proved it according to probability statistics theorem by using the method from special to general; also,basing on error distribution theorem and probability statistics theorem,the authors proved it.First,we deprived probability density of median closely according to probability density formula of Laplace distribution,from general to special; then we proved the unbiasedness of L₁ estimation according to probability density of median. When n is odd number,our reasoning thoughts are:(1) we rearrange observed values,big or small. (2) we deprive probability density of subsample according to probability density function of Laplace distribution. (3) we deprive probability density of median according to probability density of subsample. (4) we proved the unbiasedness of L₁ estimation according to probability density of median. Finally,we draw the conclusions:(1) L₁ estimation is unbiased estimation,and this conclusion shows L₁ estimation has good statistical characteristic. (2) the conclusion drawn by this method is same as that deprived from dual theorem of linear programming in reference ^[2],but,this conclusion is deprived from probability statistical theorem,it is simple and accepted easily. (3) this reasoning method can enlighten us to prove the unbiasedness of L_p estimation.

王振杰, 欧吉坤, 曲国庆. 一元Laplace分布的L1-范估计的无偏性[J]. 武汉大学学报 ● 信息科学版, 2001, 26(4): 361-363.

引用本文:

王振杰, 欧吉坤, 曲国庆. 一元Laplace分布的L₁-范估计的无偏性[J]. 武汉大学学报 ● 信息科学版, 2001, 26(4): 361-363.

WANG Zhenjie, OU Jikun, QU Guoqing. The Unbiasedness of L1 Estimation of Monistic Laplace Distribution[J]. Geomatics and Information Science of Wuhan University, 2001, 26(4): 361-363.

Citation:

WANG Zhenjie, OU Jikun, QU Guoqing. The Unbiasedness of L₁ Estimation of Monistic Laplace Distribution[J]. Geomatics and Information Science of Wuhan University, 2001, 26(4): 361-363.