回归系数一类线性估计与广义最小二乘估计的相对效率_孔胜春.pdf

3612 中 国 科 学 技 术 大 学 学 报 V ol. 36, No. 12 2 0 0 6 12 JOURNAL OF UNI VERSIT Y OF SCIENCE AND T ECHNOLOGY OF CHINA Dec. 2 0 0 6 : 0253-2778( 2006) 12-1294-05 * 孔胜春 ( , 230026) : 在均方误差矩阵准则下研究了回归系数的一类线性估 相对于广义最小二乘估 的优良性 问题, 并讨论了三种不同相对效率的上下界. : 线性回归模型; 广义最小二乘估 ; 一类线性估 ; 相对效率 : O212. 1 : A AMS Subject Classification (2000) : Prim ry 62F10; Second ry 62J05 The relative efficiencies of a class of linear estimator with respect to generalize least square estimator in linear regression mo el KONG Sheng-chun ( Sp eci al C lass f or th e G if t ed Young , Univ ers i ty of S ci ence and T ech nol ogy of Chi na, H ef ei 230026, Chi na) Abstract: The super iority of cl ss of line r estim tor w ith respect to gener lized le st squ re ( GLS) estim tor of regression coefficients w s studied in term s of the me n squ re error m trix ( M SEM) criter ion, nd the low er bound nd super bound of three rel tive efficiencies w er e obt ined respectively. Key wor s: line r r egression model; gener lized le st squ re estim tor; kind of line r estim tor; rel tive efficiencies , ( 1) GLS 0 , G uss-M r kov : , GLS Yn@ 1 = Xn@ p Bp @ 1 + en@ 1, 2 ( 1) , ( best E ( e) = 0, Cov( e) = R 2, 2