Sharper Concentration Inequalities for Median-of-Mean Processes

The Median-of-Mean (MoM) estimation is an efficient statistical method for handling data with contamination. In this paper, we propose a variance-dependent MoM estimation method using the tail probability of a binomial distribution. The bound of this method is better than the classical Hoeffding method under mild conditions. This method is then used to study the concentration of variance-dependent MoM empirical processes and sub-Gaussian intrinsic moment norm. Finally, we give the bound of the variance-dependent MoM estimator with distribution-free contaminated data.