A note on new Bernstein-type inequalities for the log-likelihood function of Bernoulli variables

Yunpeng Zhao

Statistics & Probability Letters, 2020, vol. 163, issue C

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 this 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.

Keywords: Concentration inequality; Bernstein-type inequality; Bernoulli distribution; Moment generating function (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108779

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