TY - JOUR
T1 - A note on new Bernstein-type inequalities for the log-likelihood function of Bernoulli variables
AU - Zhao, Yunpeng
N1 - Funding Information:
This research was supported by the National Science Foundation, United States of America grant DMS-1840203 . The author thanks Dr. Yizao Wang for a careful reading of an earlier draft and many helpful discussions. The author thanks the editor and an anonymous referee for their constructive feedback and corrections.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/8
Y1 - 2020/8
N2 - 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.
AB - 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.
KW - Bernoulli distribution
KW - Bernstein-type inequality
KW - Concentration inequality
KW - Moment generating function
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U2 - 10.1016/j.spl.2020.108779
DO - 10.1016/j.spl.2020.108779
M3 - Article
AN - SCOPUS:85083056690
SN - 0167-7152
VL - 163
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
M1 - 108779
ER -