摘要：We complement the results of Fourdrinier, Mezoued and Strawderman in [5] who considered Bayesian estimation of the location parameter $\theta$ of a random vector $X$ having a unimodal spherically symmetric density $f(\|x-\theta\|^{2})$ for a spherically symmetric prior density $\pi(\|\theta\|^{2})$. In [5], expressing the Bayes estimator as $\delta_{\pi}(X)=X+\nabla M(\|X\|^{2})/m(\|X\|^{2})$, where $m$ is the marginal associated to $f(\|x-\theta\|^{2})$ and $M$ is the marginal with respect to $F(\|x-\theta\|^{2})=1/2\int_{\|x-\theta\|^{2}}^{\infty}f(t)\,dt$, it was shown that, under quadratic loss, if the sampling density $f(\|x-\theta\|^{2})$ belongs to the Berger class (i.e. there exists a positive constant $c$ such that $F(t)/f(t)\geq c$ for all $t$), conditions, dependent on the monotonicity of the ratio $F(t)/f(t)$, can be found on $\pi$ in order that $\delta_{\pi}(X)$ is minimax.
