Pith Number

pith:2DKHTONW

pith:2026:2DKHTONWN6S5CHY4KGODK4DCE3

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Wasserstein-Based Test for Empirical Measure Convergence of Dependent Sequences

Alexander Yordanov, Peter Hristov

A Wasserstein-1 statistic tests convergence of empirical measures from stationary dependent sequences.

arxiv:2604.02700 v2 · 2026-04-03 · stat.AP

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We establish asymptotic level-α validity under the null, together with consistency under fixed alternatives for the statistic T_n = sqrt(n) W_1(μ̂_n, μ).

C2weakest assumption

The underlying sequence is stationary and possesses an invariant probability measure μ (implicit in the setup for both known and unknown cases).

C3one line summary

Wasserstein-based tests for empirical measure convergence in stationary dependent sequences, with asymptotic level-alpha validity for known measures and pairwise tests for unknown measures.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:04:01.353392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0d479b9b66fa5d11f1c519c35706226e6528f7a25dbaea6a84d7fe871b0c264

Aliases

arxiv: 2604.02700 · arxiv_version: 2604.02700v2 · doi: 10.48550/arxiv.2604.02700 · pith_short_12: 2DKHTONWN6S5 · pith_short_16: 2DKHTONWN6S5CHY4 · pith_short_8: 2DKHTONW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2DKHTONWN6S5CHY4KGODK4DCE3 \
  | 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: d0d479b9b66fa5d11f1c519c35706226e6528f7a25dbaea6a84d7fe871b0c264

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e898560ea702f49984c0c8d56e852079fa49192ece21b7c5585be76699e20c5a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.AP",
    "submitted_at": "2026-04-03T03:49:40Z",
    "title_canon_sha256": "3f3a65dd59d5f6c2961783f3b29d2130e87e49da615ca97807e4de8441f1969e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.02700",
    "kind": "arxiv",
    "version": 2
  }
}