共查询到16条相似文献,搜索用时 109 毫秒
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在正态-逆Wishart先验下研究了多元线性模型中参数的经验Bayes估计及其优良性问题.当先验分布中含有未知参数时,构造了回归系数矩阵和误差方差矩阵的经验Bayes估计,并在Bayes均方误差(简称BMSE)准则和Bayes均方误差阵(简称BMSEM)准则下,证明了经验Bayes估计优于最小二乘估计.最后,进行了Monte Carlo模拟研究,进一步验证了理论结果. 相似文献
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回归系数Stein压缩估计的小样本性质 总被引:10,自引:0,他引:10
本文在广义均方误差(GMSE)准则下给出了回归系数β的Stein估计优于最小二乘(LS)估计的充分必要条件,然后在Pitman Closeness(PC)准则下比较了Stein估计相对于LS估计的优良性,本文最后给出了一个特别的注记。 相似文献
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对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差.最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计. 相似文献
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错误先验假定下回归系数Bayes估计的小样本性质 总被引:15,自引:0,他引:15
本在于错误指定的先验假定获得了回归系数的Bayes估计(BE),并在均方误差矩阵准则下对其与最小二乘(LS)估计进行了比较,导出了它们的相对效率的界、讨论了在后验PitmanCloseness准则下BE相对于LS估计的优良性。 相似文献
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错误先验假定下Bayes线性无偏估计的稳健性 总被引:1,自引:0,他引:1
本文基于错误的先验假定获得了一般线性模型下可估函数的Bayes线性无偏估计(BLUE), 证明了在均方误差矩阵(MSEM)准则和后验Pitman Closeness (PPC)准则下BLUE相对于最小二乘估计(LSE)的优良性, 并导出了它们的相对效率的界, 从而获得BLUE的稳健性. 相似文献
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在均方误差矩阵(MSE-M)准则和在Pitman Closeness(PC)准则下,比较了部分根方估计相对于最小二乘估计的优良性. 相似文献
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对由两个不相关的回归方程组成的系统(y1为m维向量,y2为n维向量,m≠n),运用协方差改进技巧,提出回归系数的参数型Bayes和经验Bayes迭代估计序列.证明了Bayes迭代估计的协方差矩阵序列的单调收敛性和Bayes迭代估计序列的一致性.当误差的协方差矩阵未知时,在均方误差准则(MSE)下,证明了经验Bayes迭代估计相对于单个方程的Bayes估计的优越性.这些结果进一步表明了协方差改进方法的有效性. 相似文献
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In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator (PEBE) is constructed. The superiority of the PEBE over the least squares estimator (LSE) is investigated under the mean square error (MSE) criterion. Finally, some simulation results for the PEBE are obtained. 相似文献
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ZHANG Weiping & WEI Laisheng Department of Statistics Finance University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2005,48(7):898-903
The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under mean square error matrix (MSEM) criterion. 相似文献
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In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares(LS)estimator are investigated under mean square error matrix(MSEM)criterion. 相似文献
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The Superiorities of Simultaneous Empirical Bayes Estimation for the Regression Coefficients and Error-Variance in Linear Model 下载免费PDF全文
When the hyperparameters of prior
distribution are partly known in linear model, the simultaneous
parametric empirical Bayes estimators (PEBE) of the regression
coefficients and error variance are constructed. The superiority of
PEBE over the least squares estimator (LSE) of regression
coefficients is investigated in terms of the the mean square error
matrix (MSEM) criterion, and the superiority of PEBE over LSE of the
error variance is discussed under the the mean square error (MSE)
criterion. Finally, when all hyperparameters are unknown, the PEBE
of regression coefficients and error variance are reconstructed and
the superiority of them over LSE under the MSE criterion are studied
by simulation methods. 相似文献
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In this article,the Bayes linear unbiased estimator (BALUE) of parameters is derived for the multivariate linear models.The superiorities of the BALUE over the least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Bayesian Pitman closeness (PC) criterion. 相似文献