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方差分量估计量均方误差的最佳不变无偏估计AI 解读

An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced one-way classification…

方差分量模型中的非负最小偏差不变估计AI 解读

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translations and have minimum bias, analogously to estimation theory of mean value parameters. Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist, the one of minimum norm is characterized.…