| 许凯,何道江,徐兴忠.正态-逆Wishart先验下多元线性模型中经验Bayes估计的优良性[J].数学年刊A辑,2014,35(3):267~284 |
| 正态-逆Wishart先验下多元线性模型中经验Bayes估计的优良性 |
| Superiority of Empirical Bayes Estimators in Multivariate Linear Model withRespect to Normal-Inverse Wishart Priors |
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| DOI： |
| 中文关键词: 正态-逆Wishart先验, 矩阵$t$分布, 参数经验Bayes估计, 最小二乘估计, BMSE准则, BMSEM准则 |
| 英文关键词:Normal-inverse Wishart Priors, Matrix $t$ distribution, Parametric empirical Bayes
estimator, Least square estimator, BMSE criteria, BMSEM criteria |
| 基金项目:国家自然科学基金(No.11201005, No.11071015), 全国统计科学研究计划重点项目
&(No.2013LZ17)和安徽省自然科学基金(No.1308085QA13) |
| Author Name | Affiliation | E-mail | | XU Kai | School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui, China. | tjxxukai@163.com | | HE Daojiang | Corresponding author. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui, China. | djheahnu@163.com | | XU Xingzhong | School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China. | xuxz@bit.edu.cn |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| In this paper, the authors investigate the empirical Bayes estimation of parameters
and its superiority in multivariate linear model with respect to normal-inverse Wishart priors.
When the parameters of prior distribution are partly
unknown, the empirical Bayes estimators of the regression
coefficient matrix and the error variance matrix are constructed.
It is shown that the empirical Bayes estimators are superior to the corresponding least square estimators
under the criteria of Bayes mean square error (BMSE for short) and Bayes mean square error matrix (BMSEM for short). Finally,
a Monte Carlo simulation is carried out to verify the theoretical results. |
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