先验信息下的改进主成分估计

Improved Principal Components Estimate under Prior Information

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 modelY=XC+ε, E (ε)=0, Cov (ε,ε)=σ 2Ipossessing 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.