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Concentration inequalities of MLE and robust MLE

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  • Xiaowei Yang
  • Xinqiao Liu
  • Haoyu Wei

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. "Concentration inequalities of MLE and robust MLE," Papers 2210.09398, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:2210.09398
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    References listed on IDEAS

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    1. Huiming Zhang & Haoyu Wei, 2022. "Sharper Sub-Weibull Concentrations," Mathematics, MDPI, vol. 10(13), pages 1-29, June.
    2. Qiang Sun & Wen-Xin Zhou & Jianqing Fan, 2020. "Adaptive Huber Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 254-265, January.
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