矩阵损失下线性模型中回归系数可容许估计  

Characterization of Admissibility of Linear Estimators of Regression Coefficient in a Linear Model Under Matrix Loss Function

作　　者：侯景臣[1] 佟毅[1] 

机构地区：[1]抚顺石油学院,辽宁抚顺113001

出　　处：《抚顺石油学院学报》2001年第4期78-80,共3页Journal of Fushun Petroleum Institute

摘　　要：考虑线性模型Y =Xβ +ε ,Eε=0 ,D(ε) =σ2 V ,其中X列满秩 ,V为正定矩阵。在矩阵损失下 ,吴启光得到了回归系数 β的线性估计在非齐次线性估计类中可容许的充分必要条件 ,该定理结论与BaksalaryJK和MarkiewiczA在二次损失下所得结果在表达式上有所不同。为了得到相近的结论 ,对吴启光的结果做了进一步仔细分析 ,得到结果如下 :在矩阵损失下回归系数 β的线性估计AY +g在非齐次线性估计类中可容许当且仅当XAV对称 ,且AX =I时 g =0或AX≠I时 a∈ (0 .1)有τ(AX) (-∞ ,(a - 1) / (a +1) ]∪ [1,+∞ )。自然地 ,对 β的齐次线性估计AY在非齐次估计类中的可容许估计的等价条件为XAV对称且AX =I。这一结果能更清晰地表明在二次损失下 β的可容许估计必是在矩阵损失下的可容许估计 。Consider liner model Y=Xβ+ε,Eε=0,D(ε)=σ 2V. Where X is column full rank and V is positive definite matrix. Under matrix loss WU Qi-guang have obtained the equivalence conditions under that linear estimators of β is admissible. Comparing expressions of the theorems, WU's results are different slightly from that of Baksalary J K and Markiewicz A obtained under quadratic loss in 1985.To achieve the close conclusion, WU's qualifications are analyzed in detail and the results are as follows: AY+g is admissible for a regression coefficient vector β among the set of inhomogeneous linear estimators under matrix loss if and only if XAV is symmetric and g =0 when AX=I or when AX≠I,a∈(0,1) τ(AX) (-∞,( a-1)/(a+1)] ∪ ∪[1,∞).Naturally, AY is admissible for β among the set of inhomogeneous linear estimators if formula XAV is admissible and AX=I exist. And the theorem explains clearly that the admissible estimators for β under quadratic loss become certain one under matrix loss. Accordingly, this conclusion is helpful to study other model results. [WTHZ]

关 键 词：矩阵损失 线性模型 可容许估计 回归系数 

分 类 号：O151.51[理学—数学]