Pith Number

pith:G7B5X4OF

pith:2026:G7B5X4OFMAI7P2YHRWFPM3PEXM

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Asymptotically Optimal Tests for One- and Two-Sample Problems

Arick Grootveld, Biao Chen, Venkata Gandikota

Threshold tests of relative entropy between empirical distributions are asymptotically optimal for one- and two-sample hypothesis testing.

arxiv:2601.11727 v3 · 2026-01-16 · cs.IT · math.IT

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Claims

C1strongest claim

a similar form of Hoeffding's test, namely a threshold test of the relative entropy between the two empirical distributions is also asymptotically optimal. A strong converse for the two-sample test is also obtained.

C2weakest assumption

The analysis assumes i.i.d. sampling and works in the asymptotic regime where the number of samples tends to infinity; the proofs rely on standard large-deviation properties of empirical distributions that are not re-derived in the abstract.

C3one line summary

Hoeffding's relative entropy threshold test between empirical distributions is asymptotically optimal for both one- and two-sample hypothesis testing, with a strong converse for the two-sample case.

Receipt and verification

First computed	2026-06-12T00:07:48.830209Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37c3dbf1c56011f7eb078d8af66de4bb1761b113cbf40f7241f70bfc53f77ca2

Aliases

arxiv: 2601.11727 · arxiv_version: 2601.11727v3 · doi: 10.48550/arxiv.2601.11727 · pith_short_12: G7B5X4OFMAI7 · pith_short_16: G7B5X4OFMAI7P2YH · pith_short_8: G7B5X4OF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/G7B5X4OFMAI7P2YHRWFPM3PEXM \
  | 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: 37c3dbf1c56011f7eb078d8af66de4bb1761b113cbf40f7241f70bfc53f77ca2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4e323c1b30a0fe93235a045f254dbb52c504d5551044ba80de2bea092cce4b0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-01-16T19:20:35Z",
    "title_canon_sha256": "bed31445fe6e64786c6ecbe26be12699f6ef1823c5b28379c6231dac1196c9ee"
  },
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  "source": {
    "id": "2601.11727",
    "kind": "arxiv",
    "version": 3
  }
}