科研之友
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摘要
Let y be observation vector in the usual linear model with expectation A beta and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic a(T)y is called invariant estimator for a parametric function phi = c(T)beta if its MSE depends on beta only through phi. It is shown that aTy is admissible invariant for phi, if and only if, it is a BLUE of 0, in the case when phi is estimable with zero variance, and it is of the form k (phi) over cap, where k is an element of < 0,1 > and (phi) over cap is an arbitrary BLUE, otherwise. This result is used in the one- and two-way ANOVA models. Our paper is self-contained and accessible, also for non-specialists.
- 出版日期2014
