  The construction of objective priors is, at best, challenging for
multidimensional parameter spaces. A common practice is to assume independence
and set up the joint prior as the product of marginal distributions obtained
via "standard" objective methods, such as Jeffreys or reference priors.
However, the assumption of independence a priori is not always reasonable, and
whether it can be viewed as strictly objective is still open to discussion. In
this paper, by extending a previously proposed objective approach based on
scoring rules for the one dimensional case, we propose a novel objective prior
for multidimensional parameter spaces which yields a dependence structure. The
proposed prior has the appealing property of being proper and does not depend
on the chosen model; only on the parameter space considered.
