Concentration inequalities of MLE and robust MLE

Xiaowei Yang; Xinqiao Liu; Haoyu Wei

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arXiv · 2210.09398

Concentration inequalities of MLE and robust MLE

Xiaowei Yang·Xinqiao Liu·Haoyu Wei

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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.

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Xiaowei Yang, Xinqiao Liu, Haoyu Wei. 2022-10-17. Concentration inequalities of MLE and robust MLE. https://arxiv.org/abs/2210.09398

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