多元线性模型回归系数的Stein型估计

Stein Estimator of Regression Coefficients in the Multivariate Linear Model

本文对多元线性模型的回归系数提出了Stein型估计,可使其MSE小于LS估计。分析了选取参数矩阵K的MSE准则存在的缺陷,于是应用Q(C)准则克服这些缺陷。从理论上证明了Q(C)准则的优良性,并给出了确定C的方法。

In this paper a Stein estimator is considered. Through choosing the matrix K, we prove that the Stein estimator has more precision than LSE. It is also pointed out in this paper the criterion MSE for choosing the matrix K has several weaknesses. In order to overcome these weaknesses, the criteria Q(C) is applied to choosing the matrix K, it in cludes the criterion MSE as a special case. The good properties of criteria Q(C) are proved and discussed from theoretical point of view. The methods of determining C for pratical use are suggested