mlsanityData to 7 Oct 2026

Sub-Gaussian estimators of the mean of a random vector

arXiv 1702.00482 ↗First posted 1 Feb 2017math.ST stat.ML stat.THcited by 47

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Abstract (arXiv)

We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.

Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Feb 2017.

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Citing papers per year: 2021: 7; 2022: 9; 2023: 9; 2024: 9; 2025: 6; 2026: 7.

47 papers.

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  1. 2021Robust and Differentially Private Mean Estimationcited by 66
  2. 2021Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanismcited by 50
  3. 2021Covariance-Aware Private Mean Estimation Without Private Covariance Estimationcited by 46
  4. 2022Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guaranteescited by 30
  5. 2022Privacy Induces Robustness: Information-Computation Gaps and Sparse Mean Estimationcited by 25
  6. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  7. 2022Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variancecited by 22
  8. 2021Distribution-Free Robust Linear Regressioncited by 19
  9. 2023Rethinking Backdoor Attackscited by 14
  10. 2022Outlier-Robust Sparse Mean Estimation for Heavy-Tailed Distributionscited by 13
  11. 2024High-probability minimax lower boundscited by 11
  12. 2021On the benefits of maximum likelihood estimation for Regression and Forecastingcited by 8
35 more
  1. 2023Provable Benefit of Mixup for Finding Optimal Decision Boundariescited by 6
  2. 2023Time-Uniform Confidence Spheres for Means of Random Vectorscited by 6
  3. 2022Robust Methods for High-Dimensional Linear Learningcited by 5
  4. 2023High-dimensional Location Estimation via Norm Concentration for Subgamma Vectorscited by 5
  5. 2023Finite-Sample Symmetric Mean Estimation with Fisher Information Ratecited by 5
  6. 2025Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexitycited by 5
  7. 2026Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimescited by 5
  8. 2021Robust Online Convex Optimization in the Presence of Outlierscited by 4
  9. 2024A survey on secure decentralized optimization and learningcited by 4
  10. 2025Improved Regret Bounds for Linear Bandits with Heavy-Tailed Rewardscited by 4
  11. 2022Robust supervised learning with coordinate gradient descentcited by 3
  12. 2022On Medians of (Randomized) Pairwise Meanscited by 3
  13. 2023Robust Stochastic Optimization via Gradient Quantile Clippingcited by 3
  14. 2024Minimax Linear Regression under the Quantile Riskcited by 3
  15. 2025Regularized least squares learning with heavy-tailed noise is minimax optimalcited by 3
  16. 2024The Empirical Mean is Minimax Optimal for Local Glivenko-Cantellicited by 2
  17. 2024Robust Gradient Descent for Phase Retrievalcited by 2
  18. 2024The Broader Landscape of Robustness in Algorithmic Statisticscited by 2
  19. 2025Locally minimax optimal confidence sets for the best modelcited by 2
  20. 2021Robust Generalized Method of Moments: A Finite Sample Viewpointcited by 1
  21. 2024GROS: A General Robust Aggregation Strategycited by 1
  22. 2024Differential Private Stochastic Optimization with Heavy-tailed Data: Towards Optimal Ratescited by 1
  23. 2025Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fr'echet Mediancited by 1
  24. 2022An Efficient Minimax Optimal Estimator For Multivariate Convex Regressioncited by 0
  25. 2022Robustifying Markowitzcited by 0
  26. 2023Sparse Mean Estimation in Adversarial Settings via Incremental Learningcited by 0
  27. 2023Statistical Barriers to Affine-equivariant Estimationcited by 0
  28. 2024Subsampled Ensemble Can Improve Generalization Tail Exponentiallycited by 0
  29. 2025Efficient learning of bosonic Gaussian unitariescited by 0
  30. 2026(α,β)-Stability for Boosting Vector-Valued Predictioncited by 0
  31. 2026Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient samplingcited by 0
  32. 2026Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysiscited by 0
  33. 2026On Finite-sample Concentration of Median of Incomplete U-Statisticscited by 0
  34. 2026Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oraclecited by 0
  35. 2026Clipped or Unclipped? Finite-Sample Trade-offs for Averaged SGD under Heavy-Tailed Noisecited by 0