Pith Number

pith:CXKREENA

pith:2026:CXKREENAIH2OEIAKRLABIAU726

not attested not anchored not stored refs pending

Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes

Ivan Lau, Jonathan Scarlett

An adaptive estimator using sequential randomized 1-bit threshold queries achieves order-optimal sample complexity for mean estimation under any fixed moment bound k greater than 1.

arxiv:2604.07796 v2 · 2026-04-09 · stat.ML · cs.IT · cs.LG · math.IT · math.ST · stat.TH

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\usepackage{pith}
\pithnumber{CXKREENAIH2OEIAKRLABIAU726}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

Our estimator is (ε, δ)-PAC for any distribution with a bounded mean μ ∈ [−λ, λ] and a bounded k-th central moment E[|X−μ|^k] ≤ σ^k for any fixed k > 1. Crucially, our sample complexity is order-optimal in all such tail regimes, i.e., for every such k value.

C2weakest assumption

The distribution belongs to the class with bounded mean in [−λ, λ] and bounded k-th central moment for some fixed k>1; the analysis assumes randomized threshold queries can be chosen sequentially and adaptively without additional constraints on query implementation.

C3one line summary

An adaptive 1-bit mean estimator using sequential threshold queries achieves order-optimal sample complexity for any fixed k-th moment bound, with a necessary logarithmic penalty only when variance is finite.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-25T02:01:19.224960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15d51211a041f4e2200a8ac014029fd7819879cb6ff6319fe6b7b792401d16f6

Aliases

arxiv: 2604.07796 · arxiv_version: 2604.07796v2 · doi: 10.48550/arxiv.2604.07796 · pith_short_12: CXKREENAIH2O · pith_short_16: CXKREENAIH2OEIAK · pith_short_8: CXKREENA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CXKREENAIH2OEIAKRLABIAU726 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 15d51211a041f4e2200a8ac014029fd7819879cb6ff6319fe6b7b792401d16f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d7347f0dce7669914985a007de7f53002945548d5857138f64fc40f06f0291e",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.LG",
      "math.IT",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-04-09T04:49:21Z",
    "title_canon_sha256": "ea00505a890dd9811f91e547e7e776fdf0f5c2652b4debddfe9964290f894102"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.07796",
    "kind": "arxiv",
    "version": 2
  }
}