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通过线性组合两个给定统计量进行估计AI 解读

We consider the problems of (i) covariance adjustment of an unbiased estimator, (ii) combining two unbiased estimators, and (iii) improving upon an unbiased estimator. All these problems consist in determining a minimum dispersion linear unbiased combination of given two statistics, one of which is an unbiased estimator of a vector parameter $\mathbf{\theta} \in \mathscr{H}$, and the expectation of the other is a zero vector in the problem of covariance adjustment, is equal…

一般 Gauss–Markov 模型中保持最佳线性无偏估计的线性变换AI 解读

Under a general Gauss-Markoff model $\{\mathbf{y}, \mathbf{X,\beta, V}\}$, a necessary and sufficient condition is established for a linear transformation, $\mathbf{F}$, of the observable random vector $\mathbf{y}$ to have the property that there exists a linear function of $\mathscr{Fy}$ which is a BLUE of $\mathbf{X\beta}$. A method for deriving a required BLUE from the transformed model $\{\mathbf{Fy, FX\beta, FVF}'\}$ is also indicated.

最小二乘与最佳线性无偏估计之差的欧氏范数新界AI 解读

A new bound is established for the Euclidean norm of the difference between the least squares estimator and the best linear unbiased estimator of the vector of expectations in the general linear model. The bound is valid regardless of the rank of the dispersion matrix and is expressed in substantially simpler terms than the bounds given earlier by Haberman and by Baksalary and Kala.

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最小二乘与最佳线性无偏估计之差的欧氏范数界AI 解读

Haberman's bound for a norm of the difference between the least squares and the best linear unbiased estimators in a linear model with nonsingular covariance structure is examined in the particular case when a vector norm involved is taken as the Euclidean one. In this frequently occurring case, a new substantially improved bound is developed which, furthermore, is applicable regardless of any additional condition.