Xiaowei Yang, Xinqiao Liu, Haoyu Wei
arXiv 17 Oct 2022 · Mathematics — Statistics Theory · publishedCommunication in Statistics-Theory and Methods (2023) · 2 citations (OpenAlex)
arXiv:2210.09398 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Miao, Y (2010) Concentration inequality of maximum likelihood estimator | 0.874 | 7 | 2 | 100% |
| 2 | Maurer, A. and Pontil, M (2021) Concentration inequalities under sub-gaussian and sub-exponential conditions | 0.874 | 6 | 2 | 100% |
| 3 | Catoni, O (2012) Challenging the empirical mean and empirical variance: a deviation study | 0.644 | 2 | 2 | 100% |
| 4 | Mardia, K., Southworth, H., and Taylor, C (1999) On bias in maximum likelihood estimators | 0.644 | 2 | 2 | 100% |
| 5 | Lerasle, M (2019) Lecture notes: Selected topics on robust statistical learning theory | 0.511 | 2 | 1 | 100% |
| 6 | Weinberg, G. V (2017) Noncoherent radar detection in correlated pareto distributed clutter | 0.405 | 1 | 1 | 100% |
| 7 | Arnold, B. C (2014) Pareto distribution | 0.405 | 1 | 1 | 100% |
| 8 | Buldygin, V. V. and Kozachenko, I. V (2000) Metric characterization of random variables and random processes, volume 188 | 0.405 | 1 | 1 | 100% |
| 9 | Cramér, H (1946) Mathematical Methods of Statistics | 0.405 | 1 | 1 | 100% |
| 10 | Huber, P. J (1964) Robust estimation of a location parameter | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 17 scored citations.