具有不正确设计阵和散布阵的随机回归系数和参数的G-M估计  

G-M Estimation of Stochastic Regression Coefficient and Parameter with Incorrect Design and Dispersion Matrices

作　　者：陈建宝[1] 

机构地区：[1]云南大学统计系

出　　处：《云南大学学报（自然科学版）》1992年第3期239-247,共9页Journal of Yunnan University(Natural Sciences Edition)

摘　　要：考虑随机效应线性模型Y=Xβ+ε,E（β′,ε′）=0,Cov（（β′,ε′）′）=diag（б_1~2,б_2~2）,其中X,V≥o U≥0及A均为已知阵,α,б_1~2和б_2~2为参数,记此模型为 L（Xβ,Aα;б_1~2V,б_2~2U）,在 L（X_0β,Aα;б_1~2V_0,б_2~2U_0）下,假定X_0Aα和X_0β的G-M估计存在,我们求解下列问题:在什么条件下, L（X_0β,Aα; б_1~2V_0,б_2~2U_0）下的每个可估函数ω′_1α,ω′_2β及ω′_1α+ω′_2β的G-M估计也是L（Xβ,Aα;б_1~2V,б_2~2U）下相应待估函数的a）无偏估计;In this paper, we consider the random effects linear model Y=Xβ+ε, E (β', ε') ' = 0, Cov( (β', ε') ') =diag (δ21V, δ22U), where X, V≥0, U≥0 and A are known matrices, δ21 and δ22 are parameters, denoted this model by L (Xβ, Aα; δ21V, δ22U) . Under the model L ( X0β, Aα, δ21V0, δ22U0) , assume there exist G-M estimators of X0Aαand X0β, we provide solution to the following problems: What is the class of L (Xβ, Aα; δ21V, δ22U} such that every G-M estimator of every estimable function ω'1α, ω'2β and ω'1α+ω'2β under L (X0β, Aα; δ21V0, δ22U0) is a) an unbiased estimator; b) a G-M estimator of ω'1α, ω'2β and ω'1α+ω'2β under L (Xβ, Aα; δ21V, δ22U} respectively.

关 键 词：回归系数 参数 设计阵 散布阵 

分 类 号：O212.1[理学—概率论与数理统计]