导　　师： 王炜（火斤）

学科专业： G0101

授予学位： 硕士

作　　者： ;

机构地区： 广西师范大学

摘　　要： 线性模型中参数的相对效率是近年来讨论较多的一个问题。在线性模型的参数的估计类中，比较常见的有两种，一种称为参数的最佳线性无偏估计，另一种称为参数的最小二乘估计，由于模型误差的协方差阵在求逆时计算量大或协方差阵未知等原因，往往使用最小二乘估计代替最佳线性无偏估计，但由此将给估计精度带来一定的损失。相对效率：就是度量这种损失的一种重要方法。许多文献在一般GAUSSMARKOV模型中讨论了参数的相对效率及其相应的性质。本文在奇异线性模型下讨论了相对效率的下界及其与广义相关系数的联系等问题。考虑模型)／二X夕+[，刀([)二0。COY([)二口’∑(1)这里Y为NXL的观察向量，X为NXP的设计阵，且，(X)二，主P，P为PX1的未知参数向量，‘为NX1的随机误差向量，O-’也是未知参数，∑为非负定协方差阵且其秩为R(∑)二J三N。 THE RELATIVE EFFICIENCY OF THE LEAST SQUARES ESTIMATOR IN SINGULAR LINNEAR MODEL Wang Jie Major: Foundarnental Mathematics Graduate: Grade 97 Advicor: Prof.Wang Weixi Prof.Wang Chengrning In recent years some statisti~ns pay more attention to the relative efficiencies of parameter in Linear model. There are two important estimators: one is said the best Linear unbiased estimator. the other is the lease square estimator.are frequently used in estimation class of parameter. Because of some reason .we always use LSE instead of BLUE. This will result in loss~ to precision of estimator. So relative efficiency is introduced to measure this kind of loss. About this problem. some authors have discussed in Gauss-Markov model. In this paper, we discuss the lower bound of the relative efficiency in Singular Linear model. at the same time, the relation between relative effciency and gerneralized coefficiency of correlation are also built. We consider the Linear model YzX13±c. E/(~/)~O. Cov/(~/)~a2E /(lij where Y is an n x 1 observable random vector X is a design matrix. r/(X/) ,' < p.13 C R~. and a2 are unknown parameter. ￡ is the n x 1 random error vector. E is a dispersion matrix r/(~/) = 2 /_ n. On the basis of the theory of lease square, we know BLUE sf13. /(X'T~XyX'T-Y, where A~ is Moore-Penrose general inverse matrix T E * X'UX where U Id. /)c > 0 in this paper, r/(T/) = r/(~:X/). ifs covariance matrix is Cov/(j37/) = /(XfT~X/)4X~TT*X/(XcT~X/)~. While the lease square unbiased estimator of 13 is ~ - /(X~X/)±XIY . It's covariance matrix is Cov/(13/) = /(X'X/)+X'EX/(X'X/)+ a2 , According to Gauss-Markov theory.we know CovCi3/) /_ Cov/(8/) In more cases of application .~l is unknow or not so clear, so lease square estmator ~3 is used to replace ~. which will lead to some loss. An important way to estimate such loss is relative efficiency. Now. we-introd

关 键 词： 奇异线性模型 最小二乘估计 相对效率 协方差阵 随机误差向量

领　　域： [理学] [理学] [理学] [理学]