摘要
考虑线性模型Y=Xβ+ε,其中β和ε分别为p维和n维不可观测的随机向量,(或V);A,V为已知阵:α∈R^k和σ~2>0为参数.在二次损失和矩阵损失下,我们给出了或在齐次线性估计类(或线性估计类)中是可容许估计的充要条件.另外,当或时,在二次损失下,我们给出了在一切估计类中是可容许估计的充分条件和一些必要条件;在矩阵损失下,我们还给出了在一切估计类中是可容许估计的充要条件.
We consider the moder Y= Xβ+ ε, where β and ε are p- dimensional and n
- dimensional unobservable random vectors respectively,
≥0(or V); X, A, V are known matrices; α∈Rk and σ2> 0 are parameters. The necessary and
sufficient condition for estimate
of
to be admissible among the cla
ss of homogenous linear estimates (linear estimates) under quadratic or matrix loss function are gai
ned. when
the sufficient conditions and some nec
essary conditions for
to be admissible within the class that contains all the estimates
for
with the quadratic loss function are derived; The necessary and sufficient conditions for
estimate
of
to be admissible in the class of all estimates under matrix loss fu
nction are also given.
出处
《云南大学学报（自然科学版）》
CAS
CSCD
1990年第2期97-106,共10页
Journal of Yunnan University(Natural Sciences Edition)
关键词
回归系数
参数
线性估计
可容许性
regression coefficient, parameter, linear eshinates, loss function admissibility
