[1]邱红兵,罗季,孙旭.奇异线性模型下最小范数二次无偏估计关于误差分布的稳健性[J].华侨大学学报(自然科学版),2012,33(1):112-116.[doi:10.11830/ISSN.1000-5013.2012.01.0112]
　QIU Hong-bing,LUO Ji,SU Xu.Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance in Terms of Error Distributions under the Singular Linear Model[J].Journal of Huaqiao University(Natural Science),2012,33(1):112-116.[doi:10.11830/ISSN.1000-5013.2012.01.0112]
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奇异线性模型下最小范数二次无偏估计关于误差分布的稳健性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第1期
页码:
112-116
栏目:
出版日期:
2012-01-20

文章信息/Info

Title:
Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance in Terms of Error Distributions under the Singular Linear Model
文章编号:
1000-5013(2012)01-0112-05
作者:
邱红兵; 罗季; 孙旭
广东工业大学应用数学学院; 浙江财经学院数学与统计学院; 东北财经大学统计学院
Author(s):
QIU Hong-bing1;  LUO Ji2;  SU Xu3
1.Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China; 2.School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China; 3.School of Statistics, Dongbei University of Finance and Economics, Dalian 116025, China
关键词:
奇异线性模型;  稳健性;  最佳线性无偏估计;  最小范数二次无偏估计
Keywords:
singular linear model;  robust;  best linear unbiased estimator;  minimum norm quadratic unbiased estimator
分类号:
O212.1
DOI:
10.11830/ISSN.1000-5013.2012.01.0112
文献标志码:
A
摘要:
讨论奇异线性模型下方差σ2的最小范数二次无偏估计关于误差分布的稳健性问题,得到方差的最小范数二次无偏估计保持最优的误差项的最大分布类.进一步考虑可估计函数Xβ的最佳线性无偏估计的稳健性,得到了Xβ的最佳线性无偏估计与方差σ2的最小范数二次无偏估计同时最优的误差项的最大类.
Abstract:
Robustness of the minimum norm quadratic unbiased estimator of variance in terms of error distributions is discussed in singular linear model.We explore the maximal distribution class of error term,where the minimum norm quadratic unbiased estimator of variance σ2 holds its optimality.Furthermore considering robustness of the best linear unbiased estimator of estimable function Xβ,we obtain the maximal distribution class of error term,where the minimum norm quadratic unbiased estimator of variance σ2 and the best linear unbiased estimator of Xβ keep optimality simultaneously.

参考文献/References:

[1] RAO C R. Linear statistical inference and its applications [M]. New York:wiley, 1973.
[2] 王松桂. 线性模型的理论及其应用 [M]. 合肥:安徽教育出版社, 1987.
[3] BAKSALARY J K, KALA R. On equalities between BLUEs, WLSE, and SLSEs [J]. Canadian Journal of Statistics, 1983(2):119-123.
[4] PUNTANEN S. Some matrix results related to a partitioned singular linear model [J]. Comm Statist:Theory Methods, 1996(2):269-279.
[5] PUNTANEN S. Some further results related to reduced singular linear models [J]. Comm Statist:Theory Methods, 1997(2):375-385.
[6] WERNER H J, YAPAR C. A BLUE decomposition in the general linear regression model [J]. Linear Algebra and Its Applications, 1996.395-404.
[7] PUNTANEN S, STYAN G P H. The equality of the ordinary leas squares estimator and the best linear unbiased estimator [J]. American Statistician, 1989(3):153-161.
[8] TIAN Yong-ge, WIENSB D P. On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model [J]. Statistics & Probability Letters, 2006, (12):1265-1272.
[9] GROB J. A note on equality of MINQUE and simple estimator in the general Gauss-Markov model [J]. Statistics & Probability Letters, 1997(4):335-339.doi:10.1016/S0167-7152(97)00030-8.
[10] ZHANG Bao-xue, LUO Ji, LI Xin. Robustness of minimum norm of variance under the quadratic unbiased estimator general linear model [J]. Transactions of Beijing Institute of Technology, 2002(1):97-100.doi:10.3969/j.issn.1004-0579.2002.01.022.
[11] LI Shu-you, Zhang Bao-xue. Robustness of mnimum norm quadratic unbiased estimator of variance for the general linear model [J]. Journal of Mathematical Research and Exposition, 2004(2):280-284.doi:10.3770/j.issn.2095-2651.2004.02.015.
[12] 倪国熙. 常用的矩阵理论和方法 [M]. 上海:上海科学技术出版社, 1984.74-75.

备注/Memo

备注/Memo:
国家自然科学基金资助项目(11171058); 国家社会科学基金资助项目(11CTJ008); 浙江省自然科学基金资助项目(Y6110615)
更新日期/Last Update: 2014-03-23