Pith. sign in

REVIEW 3 cited by

Finite-sample properties of the trimmed mean

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2501.03694 v1 pith:ZE7NBFWO submitted 2025-01-07 math.ST math.PRstat.TH

Roberto I. Oliveira , Paulo Orenstein , Zoraida F. Rico This is my paper · ORCID
classification math.STmath.PRstat.TH
keywords meantrimmedsampleassumptionsfinite-samplepropertiesprovesome
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

The trimmed mean of $n$ scalar random variables from a distribution $P$ is the variant of the standard sample mean where the $k$ smallest and $k$ largest values in the sample are discarded for some parameter $k$. In this paper, we look at the finite-sample properties of the trimmed mean as an estimator for the mean of $P$. Assuming finite variance, we prove that the trimmed mean is ``sub-Gaussian'' in the sense of achieving Gaussian-type concentration around the mean. Under slightly stronger assumptions, we show the left and right tails of the trimmed mean satisfy a strong ratio-type approximation by the corresponding Gaussian tail, even for very small probabilities of the order $e^{-n^c}$ for some $c>0$. In the more challenging setting of weaker moment assumptions and adversarial sample contamination, we prove that the trimmed mean is minimax-optimal up to constants.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Robust Instrumental Variables: Sharp Rates and Inference under Adversarial Contamination

    econ.EM 2026-07 conditional novelty 7.0 of 10

    W-2SLS, a winsorized-mean version of 2SLS, attains the minimax-optimal error rate under adversarial contamination and preserves clean-sample Gaussian inference when sqrt(n) eta_n^{1-1/m} -> 0.

  2. Improved Concentration for Mean Estimators via Shrinkage

    math.ST 2025-12 conditional novelty 7.0 of 10

    A general class of shrinkage-based robust mean estimators is shown to attain near-optimal sub-Gaussian concentration whenever the base estimator has bounded error and is computed on an independent sample.

  3. Adversarially robust multiple testing in high dimensions

    math.ST 2026-07 conditional novelty 6.0 of 10

    Winsorized step-down multiple testing procedures control the familywise error rate under adversarial contamination in high-dimensional one- and two-sample mean testing with only 2+ moments.

Pith tools