Concentration inequalities of MLE and robust MLE
Xiaowei Yang, Xinqiao Liu, Haoyu Wei
TL;DR
This paper derives sharp concentration inequalities for the MLE and robust MLE under specific moment conditions, providing theoretical guarantees for their performance in statistical estimation.
Contribution
It establishes new concentration and oracle inequalities for MLE and robust MLE under exponential and second-moment conditions, respectively.
Findings
Sharp concentration inequalities for MLE under exponential moments.
Oracle inequalities for robust MLE under second-moment conditions.
Theoretical performance bounds for estimators in statistical models.
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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Taxonomy
TopicsAdvanced Statistical Methods and Models · Statistical Methods and Inference