最小二乘估计精度及其界限

The Inefficiency of the Least Squares Estimator and Its Bound

摘要: Puntanen^[1]提出用均方误差来度量最小二乘估计的精度,以后Styan^[2],Rao^[3]等相继讨论了这种精度及其界限.本文考虑采用广义方差,从而引进了一种新的最小二乘估计精度的度量并讨论了它的界.
- 精度 /
- 相对效率 /
- 均方误差 /
- 广义方差 /
- 矩阵微商 /
- 最佳线性无偏估计
Abstract: It was suggested by Pantanen^[1] that the mean squared error may be used to measure the inefficiency of the least squares estimator.Styan^[2] and Rao^[3] et al.discussed this inefficiency and it's bound later.In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.
- inefficiency /
- relative efficiency /
- mean squared error /
- generalized variance /
- matrix derivative /
- best linear unbased estimator

[1]	Puntanen,Simo,Personal communication,(1982).
[2]	Styan,G.P.H.,On some inequalities associated with ordinary least squares and the Kantorovich inequality,Festschrift for Eino Haikala on His Seventieth Birthday,Univ.of Tampere(1983),158-166.
[3]	Rao,C.R.,The inefficiency of least squares:Extensions of the Kantorovich Inequality,Linear Algebra and Its Applications,70(1985),249-255.
[4]	Bloomfield,P.,and G.S.Watson,The inefficiency of least squares,Biometrika,62(1975),121-128.
[5]	Knott,M.,On the minimum efficiency of least square,Biometrika,62(1975),129-132.
[6]	王松桂,《线性模型的理论及其应用》,安徽教育出版社(1987).
[7]	王松桂,广义相关系数与估计效率,科学通报,19(1985), 1621-1524.
[8]	杨虎,Kantorovich不等式的延拓与均方误差比效率,应用数学,4 (1988) 85-90.
[9]	Wang Song-gui(王松桂) and Yang Hu(杨虎),Kantorovich-type inequality and the measure of inefficiency of the GLSE,Acta.Math.Appli.Sinica.,5,4(1989),372-381.
[10]	杨虎、王松桂,条件数、谱范数与估计精度、应用概率统计(即将发表).
[11]	Khatri,C.G.and C.R.Rao,Some extension of the Kantorovich inequality and statistical applications,J.Multi.Anal.,11(1981),498-505.
[12]	Khatric,C.G.and C.R.Rao,Some generalizations of Kantorovich inequality,Sankhya,Ser.A.,44(1982),91-102.