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

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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.

Original languageEnglish (US)
Article number108779
JournalStatistics and Probability Letters
Volume163
DOIs
StatePublished - Aug 2020
Externally publishedYes

Keywords

  • Bernoulli distribution
  • Bernstein-type inequality
  • Concentration inequality
  • Moment generating function

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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