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Heteroscedastic errors in a linear functional relationship
线性函数关系中的异方差误差
SUMMARY We consider the estimation of structural parameters in a multivariate linear functional relationship when the error variances and covariances are not necessarily homogeneous. Estimators are obtained as roots of a system of nonlinear equations and an iterative algorithm is briefly described for finding numerical solutions of the system. Asymptotic properties of the estimators are studied and in particular an estimate of the asymptotic covariance matrix of the…
Estimation of Multivariate Linear Functional Relationships
Estimation of multivariate linear functional relationships
多元线性函数关系的估计
Consistent estimation of the structural parameters in a multivariate linear functional relationship between two vector variables observed with error is considered. When the covariance matrix of the error terms contains unknown parameters, it is shown that the usual maximum likelihood approach generally yields inconsistent estimators. A natural modification of the likelihood equations leading to a consistent estimation procedure is proposed. The connexion with estimation in…
On an Unbiased Predictor in Factor Analysis
因子分析中一个无偏预测量的讨论
For a factor analysis model in which some or all of the independent variables are subject to errors of measurement, Lawley & Maxwell (1973) claim to have obtained an unbiased predictor of the dependent variable based on the independent variables. This predictor is shown to be biased and an alternative unbiased estimator with minimum mean squared error is derived.
On an unbiased predictor in factor analysis
因子分析中的无偏预测器
For a factor analysis model in which some or all of the independent variables are subject to errors of measurement, Lawley & Maxwell (1973) claim to have obtained an unbiased predictor of the dependent variable based on the independent variables. This predictor is shown to be biased and an alternative unbiased estimator with minimum mean squared error is derived.
Best Linear Unbiased Estimates of the Parameters of the Logistic Distribution Based on Selected Order Statistics
基于选定次序统计量的 Logistic 分布参数最优线性无偏估计
Coefficients, variances and efficiencies are provided for the best linear unbiased estimates (BLUE's) of the mean and standard deviation of the logistic distribution, with both unknown, based on four order statistics with ranks giving the maximum joint efficiency among all BLUE's based on four order statistics. Asymptotic joint efficiencies are compared for asymptotically best linear estimates (ABLE's) based on order statistics with ranks determined by various spacings. With…