| 具有未知误差方差的多元正态线性模型中回归系数的所有k-容许估计 |
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| 引用本文： | 邓起荣,陈建宝.具有未知误差方差的多元正态线性模型中回归系数的所有k-容许估计[J].数学学报,1998,41(2):385-392. |
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| 作者姓名： | 邓起荣 陈建宝 |
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| 作者单位： | [1]云南教育学院数学系 [2]云南大学统计系 |
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| 基金项目： | 云南省应用基础研究基金 |
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| 摘 要： | 考虑多元线性模型Ｙ～Ｎ（ＸΘ，σ２ＩｍＶ），和ＳＸΘ的估计问题，取损失函数为（σ－ＳＸΘ）′（δ－ＳＸΘ），本文定义所谓的ｋ－容许性和Φ（ｋ）－容许性．本文在一定条件下得到了ＳＸΘ的线性估计ＬＹ＋Ｄ在一切估计类中ｋ－容许和Φ（ｋ）－容许的充要条件．一般情况下得到了充分条件和必要条件．
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| 关 键 词： | 多元正态线性模型，未知方差，k－容许，Φ（k）－容许 |
| 收稿时间： | 1996-5-3 |
| 修稿时间： | 1997-4-2 |
All k -Admissible Estimators of Regression Coefficients in Multivariate Normal Linear Models with Unknown Error Variance |
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| Deng Qirong.All k -Admissible Estimators of Regression Coefficients in Multivariate Normal Linear Models with Unknown Error Variance[J].Acta Mathematica Sinica,1998,41(2):385-392. |
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| Authors: | Deng Qirong |
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| Institution: | Deng Qirong ( Department of Mathematics, Education College, Kunming 650223 , China ) Chen Jianbao ( Department of Statistics, Yunnan University, Kunming 650091 , China ) |
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| Abstract: | Consider the multivariate linear model Y～N(XΘ,σ 2I mV) , and the estimation problem of SXΘ ,selecting the loss as (δ-SXΘ)′(δ-SXΘ) We have defined the so-called k -admissibility and Φ(k) -admissibility can be defined. The necessary and sufficient conditions, under some restriction, for the estimator LY+D of SXΘ to be k -admissible and Φ(k) -admissible are obtained,respectively. For general case the necessary conditions and sufficientconditions are also given. |
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| Keywords: | Multivariate normal linear models Unknown error variance k -admissible Φ(k) -admissible |
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