Do we need to estimate the variance in robust mean estimation?
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909080818286592 |
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| author | Sun, Qiang |
| author_facet | Sun, Qiang |
| contents | In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean parameter and a robustification parameter. By jointly optimizing the empirical loss function with respect to both parameters, the robustification parameter estimator can automatically adapt to the unknown data variance, and thus the self-tuned mean estimator can achieve optimal finite-sample performance. Our method outperforms previous approaches in terms of both computational and asymptotic efficiency. Specifically, it does not require cross-validation or Lepski's method to tune the robustification parameter, and the variance of our estimator achieves the Cramér-Rao lower bound. Project source code is available at \url{https://github.com/statsle/automean}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_00118 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Do we need to estimate the variance in robust mean estimation? Sun, Qiang Methodology Statistics Theory In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean parameter and a robustification parameter. By jointly optimizing the empirical loss function with respect to both parameters, the robustification parameter estimator can automatically adapt to the unknown data variance, and thus the self-tuned mean estimator can achieve optimal finite-sample performance. Our method outperforms previous approaches in terms of both computational and asymptotic efficiency. Specifically, it does not require cross-validation or Lepski's method to tune the robustification parameter, and the variance of our estimator achieves the Cramér-Rao lower bound. Project source code is available at \url{https://github.com/statsle/automean}. |
| title | Do we need to estimate the variance in robust mean estimation? |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2107.00118 |