2016/11/12 by Xiequan Fan, Fan, Xiequan
Mathematics · Physics and Astronomy · #60E15 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Statistical Mechanics and Entropy #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1611.03990
openalex publication_date 2016/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We improve the rate function of McDiarmid's inequality for Hamming distance. In particular, applying our result to the separately Lipschitz functions of independent random variables, we also refine the convergence rate function of McDiarmid's inequality around a median. Moreover, a non-uniform bound for the distance between the medians and the mean is also given. We also give some extensions of McDiarmid's inequalities to the case of nonnegative functionals of dependent random variables.