Concentration inequalities of MLE and robust MLE

Xiaowei Yang, Xinqiao Liu and Haoyu Wei

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 19, 6944-6956

Abstract: The Maximum Likelihood Estimator (MLE) serves an important role in statistics and machine learning. In this article, for i.i.d. variables, we obtain constant-specified and sharp concentration inequalities and oracle inequalities for the MLE only under exponential moment conditions. Furthermore, in a robust setting, the sub-Gaussian type oracle inequalities of the log-truncated maximum likelihood estimator are derived under the second-moment condition.

Date: 2024
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DOI: 10.1080/03610926.2023.2253945

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