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Information theoretic limits of robust sub-Gaussian mean estimation under star-shaped constraints

Akshay Prasadan & Matey Neykov

Annals of Statistics2026https://doi.org/10.1214/25-aos2576preprint
AJG 4*ABDC A*
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0.37

Abstract

We obtain the minimax rate for a mean location model with a bounded star-shaped set K⊆Rn constraint on the mean, in an adversarially corrupted data setting with Gaussian noise. We assume an unknown fraction ϵ≤1/2−κ for some fixed κ∈(0,1/2] of N observations are arbitrarily corrupted. We obtain a minimax risk up to proportionality constants under the squared ℓ2 loss of max(η∗2,σ2ϵ2)∧d2 with η∗=sup{η≥0:Nη2 σ2≤logMKloc(η,c)}, where logMKloc(η,c) denotes the local entropy of the set K, d is the diameter of K, σ2 is the variance and c is some sufficiently large absolute constant. A variant of our algorithm achieves the same rate for settings with known or symmetric sub-Gaussian noise, with a smaller breakdown point, still of constant order. We further study the case of unknown sub-Gaussian noise and show that the rate is slightly slower: max(η∗2,σ2ϵ2log(1/ϵ))∧d2. We generalize our results to the case when K is star-shaped but unbounded.

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@article{akshay2026,
  title        = {{Information theoretic limits of robust sub-Gaussian mean estimation under star-shaped constraints}},
  author       = {Akshay Prasadan & Matey Neykov},
  journal      = {Annals of Statistics},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aos2576},
}

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0.37

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.16 × 0.4 = 0.06
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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