Abstract
The geometric median is a very robust method for estimating parameters of location. The eciency of this method is however rather poor.
It was shown that the eciency can be improved by averaging of chosen observations, which lie in some sense around the original estimate. For this purpose we employ the median absolute deviation.
The next step to improve the eciency, which is introduced in the paper, is to employ weights for observations according to their distance from the original estimate and then to compute the weighted mean. This approach is similar to the one of M estimates.
Further we deal with a generalization of boxplot for multidimensional case. We suggest procedure based on the mentioned methods.
This leads us to looking for quantiles, where we use a similar approach which was established by Koenker and Bassett. Since there is a direct connection between robust statistic and appearance of extreme events in a sense of economic prot we deal with analogy between the value at risk and the observations which were classied as outliers by our method.
The simulation study which compares our method with other kinds of estimates is also include
