Pith Number

pith:RXSRGA4B

pith:2026:RXSRGA4BIOKOELMLZIQ4TIILAC

not attested not anchored not stored refs pending

Empirical Bernstein Confidence Intervals for Kernel Smoothers: A Safe and Sharp Way to Exhaust Assumed Smoothness

Sven Klaassen, Zihao Yuan

Empirical Bernstein calibration produces kernel smoother intervals that attain nominal coverage and minimax widths by treating bias on the original scale.

arxiv:2605.03781 v3 · 2026-05-05 · math.ST · stat.TH

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\pithnumber{RXSRGA4BIOKOELMLZIQ4TIILAC}

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Claims

C1strongest claim

Uniformly over functions with S-th order local smoothness, both one-sided and two-sided intervals attain the nominal coverage level up to a remainder of order n^{-2S/(2S+1)}, or an exponential remainder in bounded or sub-Gaussian settings. Their widths shrink at the minimax rate n^{-S/(2S+1)}.

C2weakest assumption

The target function lies in a local Taylor-remainder class with exactly S-th order smoothness, and the kernel and bandwidth satisfy the conditions needed for the bias-aware radius construction and empirical Bernstein bounds to apply.

C3one line summary

Empirical Bernstein confidence intervals for kernel smoothers attain nominal coverage up to a remainder of order n to the minus 2S over 2S+1 while achieving minimax optimal widths under S-th order local smoothness.

Receipt and verification

First computed	2026-05-28T01:04:41.545679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8de51303814394e22d8bca21c9a10b00942b3d18728882470253be03b239c464

Aliases

arxiv: 2605.03781 · arxiv_version: 2605.03781v3 · doi: 10.48550/arxiv.2605.03781 · pith_short_12: RXSRGA4BIOKO · pith_short_16: RXSRGA4BIOKOELML · pith_short_8: RXSRGA4B

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RXSRGA4BIOKOELMLZIQ4TIILAC \
  | 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: 8de51303814394e22d8bca21c9a10b00942b3d18728882470253be03b239c464

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6a8012855f5b4ca2d36f9ee9998ae0bcb6e4c9b41a4389e693a68e3d85f65de",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-05T14:08:27Z",
    "title_canon_sha256": "3c3400d338e330eca97bc5e82b75dd590c22a8d0efc8d8aa2f8b92a86f8db4e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03781",
    "kind": "arxiv",
    "version": 3
  }
}