摘要
对于线性模型Y=XC+ε,E(ε)=0,Cov(ε,ε)=σ2I,在先验信息(E(C)=0,Cov(C,C)=σ20I)下,本文给出主成分个数的一种更合理取法,并提出了一种改进的主成分估计。文中证明了该估计是可容许估计,且在“平均”均方误差意义下,优于最小二乘估计。
With regard to the linear modelY=XC+ε, E (ε)=0, Cov (ε,ε)=σ 2Ipossessing the prior information:E(C)=0, Cov (C,C)=σ 2 0I,This article gives a best method of selecting the principal components' numbers in the principal components estimate and presents an improved principal components estimate.Theoretically,we prove that the improved estimate is admissible amd that it is marked much letter than Least Square Estimate and is better than the principal components estimate in a sense of “average” error of mean square.Simulation verifies the inference above.
出处
《国防科技大学学报》
EI
CAS
CSCD
1997年第2期107-113,共7页
Journal of National University of Defense Technology
关键词
线性模型
先验信息
主成分估计
数理统计
linear model,prior information,improved principal components estimate,admissible,“average” error of mean square.