A new perspective on robust $M$-estimation: Finite sample theory and applications to dependence-adjusted multiple testing
稳健M估计的新视角：有限样本理论与依赖调整多重检验
(1973) 799-821], robust alternatives to the method of least squares are sorely needed. To achieve robustness against heavy-tailed sampling distributions, we revisit the Huber estimator from a new perspective by letting the tuning parameter involved diverge with the sample size. In this paper, we develop nonasymptotic concentration results for such an adaptive Huber estimator, namely, the Huber estimator with the tuning parameter adapted to sample size, dimension, and the…