M-estimation with e-statistics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913171003932672 |
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| author | Wang, Hongjian Ramdas, Aaditya |
| author_facet | Wang, Hongjian Ramdas, Aaditya |
| contents | We present a theory of point estimation with e-statistics (e-values and e-processes) by introducing the "ME-estimator": the parameter that minimizes the corresponding e-statistic, or the evidence against it. Our approach is based on the intuitive idea of e-statistics as a measure of evidence and betting pay-off, and naturally generalizes the classical method of maximum likelihood estimation. First, we establish the consistency as well as the almost sure convergence rate for ME-estimators relating to the high-probability bounds on the size of the confidence set derived from thresholding the e-statistics, an approach that sets ME-estimators apart from traditional M-estimators. Second, we conduct classical M-estimator-style analysis on the consistency and asymptotic normality of ME-estimators in the bounded mean estimation setting, discussing the notion of efficiency (or lack thereof) from various choices of betting strategy. Our work brings e-statistics, a fundamental tool for inference and uncertainty quantification, to the space of estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30485 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | M-estimation with e-statistics Wang, Hongjian Ramdas, Aaditya Methodology Statistics Theory We present a theory of point estimation with e-statistics (e-values and e-processes) by introducing the "ME-estimator": the parameter that minimizes the corresponding e-statistic, or the evidence against it. Our approach is based on the intuitive idea of e-statistics as a measure of evidence and betting pay-off, and naturally generalizes the classical method of maximum likelihood estimation. First, we establish the consistency as well as the almost sure convergence rate for ME-estimators relating to the high-probability bounds on the size of the confidence set derived from thresholding the e-statistics, an approach that sets ME-estimators apart from traditional M-estimators. Second, we conduct classical M-estimator-style analysis on the consistency and asymptotic normality of ME-estimators in the bounded mean estimation setting, discussing the notion of efficiency (or lack thereof) from various choices of betting strategy. Our work brings e-statistics, a fundamental tool for inference and uncertainty quantification, to the space of estimation. |
| title | M-estimation with e-statistics |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2605.30485 |