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

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  • Zhao, Yunpeng

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.

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  • Zhao, Yunpeng, 2020. "A note on new Bernstein-type inequalities for the log-likelihood function of Bernoulli variables," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220300821
    DOI: 10.1016/j.spl.2020.108779
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    References listed on IDEAS

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    1. D. S. Choi & P. J. Wolfe & E. M. Airoldi, 2012. "Stochastic blockmodels with a growing number of classes," Biometrika, Biometrika Trust, vol. 99(2), pages 273-284.
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