A complete class theorem for estimating a noncentrality parameter
The author shows that an admissible estimator \(\delta_ 0\) of the noncentrality parameter \(\theta\) of a noncentral \(\chi^ 2\) distribution which has the property \(R(\theta_ 1\delta_ 0)=O(\theta^ k)\) as \(\theta\to \infty\) for some k must be generalized Bayes. Further, the class of generalized Bayes rules satisfying this condition is complete relative to the class of all rules satisfying it. The result is applied to show inadmissibility of \(\delta_ 0(x)=(x-n)^+\) where n is the number of degrees of freedom. Another application demonstrates inadmissibility of \(\delta_ a(z)=a\{(m-z)z-n\}^+\) (a\(\neq 0)\) as an estimator of the noncentrality parameter of the noncentral F distribution with \(m\geq 5\) and n degrees of freedom.
scientific article; zbMATH DE number 4020186