Robust $M$-Estimators of Multivariate Location and Scatter

Let \mathbf{x}_1,\cdots, \mathbf{x}_nbe a sample from an mvariate distribution which is spherically symmetric up to an affine transformation. This paper deals with the robust estimation of the location vector \mathbf{t}and scatter matrix \mathbf{V}by means of "Mestimators," defined as solutions of the system: \sum_i u_1(d_i)(\mathbf{x}_i - \mathbf{t}) = \mathbf{0}and $n^{-1}\sum_i u_2(d_i^2)(\mathbf{x}_i -...