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 ${𝐚}^T𝐲$ 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 ${𝐚}^T𝐲$ is admissible invariant for $\phi$, if and only if, it is a BLUE of $\phi ,$ in the case when $\phi$ is estimable with zero variance, and it is of the form $k\widehat{\phi }$, where $k\in 〈0,1〉$ and $\widehat{\phi }$ is an arbitrary BLUE, otherwise. This result is used in...

The study of decision making and problem solving has attracted much attention. Since the middle of this century the notion of rational decision making was associated with expected utility maximization, albeit in a very different way than D. Bernoulli (1738) envisioned. For decisions under risk, Von Neumann and Morgenstern (1947) formulated the axioms for expected utility. For decisions under uncertainty Savage (1954) developed the axioms leading simultaneously to subjective probability and expected...