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．
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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1998年第2期385-392,共8页
Acta Mathematica Sinica：Chinese Series
基金
云南省应用基础研究基金
关键词
线性模型
多元线性模型
k容许估计
回归系数
Multivariate normal linear models, Unknown error variance, k -admissible, Φ(k) -admissible
