  We consider a robust estimation of the mean vector for a sequence of i.i.d.
observations in the domain of attraction of a stable law with different indices
of stability, $DS(\alpha_1, \ldots, \alpha_p)$, such that $1<\alpha_{i}\leq 2$,
$i=1,\ldots,p$. The suggested estimator is asymptotically Gaussian with unknown
parameters. We apply an asymptotically valid bootstrap to construct a
confidence region for the mean vector. A simulation study is performed to show
that the estimation method is efficient for conducting inference about the mean
vector for multivariate heavy-tailed distributions.
