Generalized Least Squares Estimators in the Analysis of Covariance Structures.
Generalized Least Squares Estimators in the Analysis of Covariance Structures.
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DOI：
10.1002/j.2333-8504.1973.tb00197.x
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发表时间：
1973-06
期刊：
影响因子：
3
通讯作者：
M. Browne
中科院分区：
文献类型：
--
作者：
M. Browne
摘要让S表示协方差矩阵Σ0的通常无偏估计，其元素是参数向量的函数。的广义最小二乘(G.L.S)估计可以通过最小化来获得，其中V是某个正定矩阵。仅在满足一定的正则性条件和S的极限分布是带特定参数的多元正态分布的条件下，研究了G.L.S估计的渐近性质。通过最大化Wishart似然函数得到的估计量(M.W.L.估计量)是一类具有最小渐近方差的G.L.S.估计量。在随机收敛到M.W.L.估计量的G.L.S.估计量中，When是线性的，所需的计算量要少得多。给出了某些线性模型的估计、离散阵的估计和检验统计量的计算方法。
SUMMARY Let S represent the usual unbiased estimator of a covariance matrix, Σ0, whose elements are functions of a parameter vector . A generalized least squares (G.L.S) estimate, of may be obtained by minimizing where V is some positive definite matrix. Asymptotic properties of the G.L.S. estimators are investigated assuming only that satisfies certain regularity conditions and that the limiting distribution of S is multivariate normal with specified parameters. The estimator of which is obtained by maximizing the Wishart likelihood function (M.W.L. estimator) is shown to be a member of the class of G.L.S. estimators with minimum asymptotic variances. When is linear in a G.L.S. estimator which converges stochastically to the M.W.L. estimator involves far less computation. Methods for calculating estimates of , estimates of the dispersion matrix of , and test statistics, are given for certain linear models.