Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables

Abstract

Abstract This paper aims to establish distribution-free concentration inequalities for the log-likelihood function of Bernoulli variables, which means that the tail bounds are independent of the parameters. Moreover, Bernstein’s and Bennett’s inequalities with optimal constants are obtained. The simulation study shows significant improvements over the previous results.

Keywords

• Bernstein’s inequality
• Bennett’s inequality
• Log-likelihood function
• Bernoulli distribution