Stein estimation for non-normal spherically symmetric location families in three dimensions
Suppose the random vector \(X=(X_ 1,X_ 2,X_ 3)'\) has density \(f(\| X-\theta\|^ 2)\) for \(\| X-\theta\|^ 2>R\) with \(f(t)\leq M<\infty\). The authors use Stein's integration by parts technique to find estimators of \(\theta\), with respect to quadratic loss. They find values of \(a\) for which the James-Stein estimator \(\delta_ a(x)=(1-a/X'X)X\) and \(\delta_{a,r}(x)=(1-a(Y(X'X)/X'X))X\) improve on \(X\).
scientific article; zbMATH DE number 404623
scientific article