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多元线性模型中回归系数的线性可容许估计 被引量：2

Admissibility for Linear Estimators to Regression Coefficients in a Multivariate Linear Models
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摘要 基于Zellner的平衡损失的思想,本文提出了矩阵形式的平衡损失函数,并在该损失函数下讨论了多元回归系数线性估计的可容许性.给出了六种不同形式的可容许定义,证明了这六种容许性在齐次和非齐次线性估计类中是一致的,且得到了其共同的可容许估计的充要条件. In this paper the matrix balanced loss functions are proposed according to Zellner＇s thought of balanced loss. Admissible linear estimators for regression coefficients in a multivariate linear model are investigated under the matrix balanced loss function under six kinds of definitions for admissibility. The six kinds of admissibility are proved to be identical in a class of homogeneous and nonhomogeneous linear estimators, and the sufficient and necessary conditions that linear estimators are admissible are obtained.
作者 曹明响 孔繁超
机构地区 合肥师范学院数学系 安徽大学数学科学学院
出处 《应用数学学报》 CSCD 北大核心 2009年第5期951-957,共7页 Acta Mathematicae Applicatae Sinica
基金 安徽省高等学校优秀青年人才基金项目(2009SQRZ154)
关键词 多元线性模型 矩阵平衡损失函数 线性估计 可容许性 multivariate linear model matrix balanced loss function linear estimators admissibility
分类号 O212.4 [理学—概率论与数理统计]
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参考文献7

  • 1Zellner. Bayesian and Non-Bayesian Estimation Using Balanced Loss Function. In: Gupta, S.S., Berger, J.O.(Eds.), Statistical Decision Theory and Related Topics V. Spring, 1994, 377-390.
  • 2Chung Y, Kim C. Simultaneous Estimation of the Multivariate Normal Mean under Balanced Loss Function. Commun. Statist-Theory Meth., 1997, 26:1599-1611.
  • 3Gruber M H J. The Efficiency of Shrinkage Estimators with Respect to Zellner's Balanced Loss Function. Commun. Statist-Theory Meth., 2004, 33(2): 235-249.
  • 4Xu X Z, Wu Q G. Linear Admissible Estimators of Regression Coefficient under Balanced Loss. Acta Math. Scientia, 2000, 20(4): 468-473.
  • 5Xie M Y. Admissibility for Linear Estimates on Multivariate Regression Coefficients. Chin. Sci. Bull., 1989, 34(19): 1448-1450.
  • 6Von Rosen D. Moments and Some Asymptotic Results for Maximum Likelihood Estimates in Multivariate Linear Normal Model with Special References to the Growth Curve Models. Research Reports No.141. List of Actuax Mathematics and Math. statistics Universities of stockholem Swedem, 1985.
  • 7Dong L M, Wu Q G. The Sufficient and Necessary Conditions of Admissible Linear Estimates for Random Regression Coefficients and Parameters under the Quadratic Loss Function. Acta Math. Sinica, 1988, 31(2): 145-157.

同被引文献15

  • 1罗汉,柏超.线性模型中参数的平衡LS估计及其性质[J].湖南大学学报（自然科学版）,2006,33(2):122-124. 被引量：12
  • 2ZELLNER A. Bayesian and non-Bayesian estimation using balanced loss functions[C]. On Statistical Decision Theory and Related Topics V. New York : Springer, 1994 : 377 - 390.
  • 3WAN A T K. On generalized ridge regression estimations under collinerity and balanced loss[ J ]. Appl Math Comp, 2002, 129:204 -212.
  • 4GILES J A, OHTANI K. The exact risk of some pretests and Stein type regression estimations under balanced loss[ J ]. Commu Statist Theory Methods, 1996,25:901 - 919.
  • 5BANSAL A K, AGGARWAL P. Bayes prediction for a heteroscedastic regression surperpopulation model using balanced loss function [ J ]. Com- mun Stat Theory Methods, 2007, 36(8) : 1565 -1575.
  • 6BANSAL A K, AGGARWAL P. Bayes prediction of the regression coefficient in a finite population using balanced loss function[J]. Metron, 2009, 67(1): 1-16.
  • 7BANSAL A K, AGGARWAL P. Bayes prediction for a stratified regression superpopulation model using balanced loss function [ J ]. Commun Stat Theory Methods, 2010, 39 : 2789 - 2799.
  • 8JOZANI M J, MARCHAND E, PARSIAN A. Bayesian and Robust Bayesian analysis under a general class of balanced loss function[ J]. Star Pa- Pers. 2012. 53:51 -60.
  • 9HUG K, PENG P. Admissibility for linear estimators of regression coefficient in a general Gauss-Markov model under balanced loss function[ J ] J Stat Plan Infer, 2010, 140:3365 -3375.
  • 10HUG K, PENG P. All admissible linear estimators of a regression coefficient under a balanced loss function [J]. J Multivariate Anal, 2011 102:1217 - 1224.

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应用数学学报
2009年 第5期

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