Is there a known way to extend (at least some) robust location estimators to multidimensional case, possibly in an efficient manner?
For example, I know that, given a list of scalars $x_1, ..., x_n$, the point x* which minimizes the sum of Huber loss over the list is a robust estimation of the location.
If I am given a list of points in $R^d$ instead of scalars, how should I modify the optimization problem?