Robust $M$-Estimators of Multivariate Location and Scatter
多元位置与散布矩阵的稳健 M 估计
Let $\mathbf{x}_1,\cdots, \mathbf{x}_n$ be a sample from an $m$-variate 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 "$M$-estimators," defined as solutions of the system: $\sum_i u_1(d_i)(\mathbf{x}_i - \mathbf{t}) = \mathbf{0}$ and $n^{-1}\sum_i u_2(d_i^2)(\mathbf{x}_i - \mathbf{t})(\mathbf{x}_i - \mathbf{t})' = \mathbf{V}$…