Higher-Order Infinitesimal Robustness
高阶无穷小稳健性
Using the von Mises expansion, we study the higher-order infinitesimal robustness of a general M-functional and characterize its second-order properties. We show that second-order robustness is equivalent to the boundedness of both the estimator’s estimating function and its derivative with respect to the parameter. It implies, at the same time, (i) variance robustness and (ii) robustness of higher-order saddlepoint approximations to the estimator’s finite sample density.…