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超结构关系：函数关系与结构关系的综合AI 解读

A maximum likelihood solution is presented for a model which is a synthesis of the linear functional and structural relations. In the replicated case, the slope estimate is a root of a quadratic equation, the coefficients of which are symmetrical with respect to the within and between-groups sample covariances. In the unreplicated case it is shown that two variance ratios must be known, whereupon the slope estimator is a root of a quintic equation. When one of these variance…

非线性函数关系的广义最小二乘与最大似然估计AI 解读

Summary A non-linear functional relationship between two mathematical variables is postulated. Departures of observed random variates from the mathematical variable values are assumed to have zero mean and general but known covariance matrix. Assuming normality we obtain by maximum likelihood an expression for the asymptotic covariance matrix of the structural parameter estimates. The expression involves a certain matrix Ψ. A generalized least squares method is proposed…

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