Robust M-Tests
研究了基于M估计的多维检验的局部稳健性，发现若估计量的影响函数无界，观测分布的微小扰动会严重扭曲检验的渐近水平和功效，并论证了基于最优有界影响估计的检验的渐近可容许性。
This paper investigates the local robustness properties of a general class of multidimensional tests based on M -estimators. These tests are shown to inherit the efficiency and robustness properties of the estimators on which they are based. In particular, it is shown that small perturbations of the distribution of the observations can have arbitrarily large effects on the asymptotic level and power of tests based on estimators that do not possess a bounded influence function. An asymptotic ‘admissibility’ result is also presented, which provides a justification for tests based on optimal bounded-influence estimators.