关键词：方差
张立振 徐兴忠
（青岛海洋大学数学系，青岛，266071） (北京理工大学，北京，100081)
摘 要 研究协方差阵Σ的二次型容许估计问题。设y1,y2,…,yn iid,n≥2,y1与p维正态分布N(β，Σ)有相同的前四阶矩。其中β=(β1,β2,…,βp)′∈Rp与Σ=(σij)p×p＞0均未知。记y =Δ(y1,y2,…,yn)′。在二次损失L(d,Σ)=tr(d-Σ)2下给出Σ的二次型估计
aS2+nby-y-′是容许估计的必要条件为：(n-1)a+b+2max(a,b)≤1。此必要条件比张立振等协方差阵的二次型容许估计中的必要条件有了明显的加强。
关键词 容许性；二次型估计；损失函数；风险函数；协方差阵
中图法分类号 O212 文章编号 1001-1862(2002)02-325-04
A Necessary Condition of the Quadratic Admissible Estimate for Covariance Matrix
Zhang Lizhen1 Xu Xingzhong2
(1 Applied Mathematics Department, Ocean University of Qingdao, Qingdao 266071, China)
(2 Mathematics Department, Beijing Institate of Technology, Beijing, 100081, China)
Abstract The quadratic admissible estimate for covariance matrix Σ is studied. Suppose that y1,y2,…,yn idd, n≥2 and y1have the first four moments as Np(β,Σ). Where both β=(β1,β2,…,βp)′∈Rp and Σ=(σij)p×p＞0 are unknown .Denote y
=△(y1,y2,…,yn)′.We choose L(d,Σ)=tr(d-Σ)2to be the loss function. A necessary condition that aS2+nby-y-′is an admissible estimate for covariance matrix Σ is (n-1)a+b+2max(a,b)≤1.
Key words admissibility; the quadratic estimate; the loss function; the risk function; the covariance matrix
AMS：62H12
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