Minimax Variance $M$-Estimators of Location in Kolmogorov Neighbourhoods
柯尔莫哥洛夫邻域中的极小极大方差位置 M 估计
We exhibit those distributions with minimum Fisher information for location in various Kolmogorov neighbourhoods $\{F|\sup_x|F(x) - G(x)| \leq \varepsilon\}$ of a fixed, symmetric distribution $G$. The associated $M$-estimators are then most robust (in Huber's minimax sense) for location estimation within these neighbourhoods. The previously obtained solution of Huber (1964) for $G = \Phi$ and "small" $\varepsilon$ is shown to apply to all distributions with strongly…