A Note on New Bernstein-type Inequalities for the Log-likelihood Function of Bernoulli Variables
Probability
2020-03-31 v2 Information Theory
math.IT
Statistics Theory
Statistics Theory
Abstract
We prove a new Bernstein-type inequality for the log-likelihood function of Bernoulli variables. In contrast to classical Bernstein's inequality and Hoeffding's inequality when applied to the log-likelihood, the new bound is independent of the parameters of the Bernoulli variables and therefore does not blow up as the parameters approach 0 or 1. The new inequality strengthens certain theoretical results on likelihood-based methods for community detection in networks and can be applied to other likelihood-based methods for binary data.
Cite
@article{arxiv.1909.00250,
title = {A Note on New Bernstein-type Inequalities for the Log-likelihood Function of Bernoulli Variables},
author = {Yunpeng Zhao},
journal= {arXiv preprint arXiv:1909.00250},
year = {2020}
}
Comments
Accepted by Statistics & Probability Letters