Bootstrapping the Mean Vector for the Observations in the Domain of Attraction of a Multivariate Stable Law

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, $DS({\alpha }_1,\dots ,{\alpha }_p)$, such that $1<{\alpha }_i\le 2$, $i=1,\dots ,p$. 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.