Before revision:  At the end, an exhaustive simulation study and an application to real data are provided where the proposed estimator is compared with known benchmarks from the literature  .
After revision:  At the end, an exhaustive simulation study and an application to real data are provided where the proposed estimator is compared with known benchmarks from the literature . It turns out that the existent estimators of the mean vector including the suggested one converge to the sample mean vector when the true mean vector possesses unbounded Euclidean norm .