摘要
考虑线性模型Y_(n×1)=X_(n×p)β_(p×1)+l,其中l～N_n(o,V),X_(n×p),V_(n×n)已知,β∈R^n。假设Kβ线性可估,在损失函数(d—Kβ)′(d—Kβ)下,本文得出了Ay在所有线性估计类中为Ky的可容许估计的充分必要条件。进一步假设Y_(n×1)～N_n(β,V),β_(n×1),V_(n×n)未知,Sβ可估,对于损失函数(d—Sβ)′(d—Sβ),本文又得出了Ay在所有估计类中为Sβ的可容许估计的充分条件。
Consider the linear model for a single measurement: y_(n×1)=X_(n×p)β_(p×1) +l_(n×1), where l has an n-variate nomal distribution N (0, C), n×p matrix X and V>0 are known. β∈R^n, Let Kβ be linear estimable. The neccessary and sufficient condition for Ay to be an admissible estimate for Kβ in the class containing all the homogeneous linear functions of observation under the loss function (d-Kβ)'(d-Kβ) is derived.Moreover, suppose y has an n-variate nomal distribution N_N(β, V), β and V>0 are unknown, let Sβ be estimable. For the loss function (d-Sβ)'(d-Sβ) the sufficient condition for Ay to be an admissible estimate for Sβ within the class containing all the estimates for Sβ is given.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
1989年第4期494-498,共5页
Journal of Central China Normal University：Natural Sciences
