Pith Number

pith:ZIWCQ423

pith:2026:ZIWCQ423H276OLX7WMWI6OVL2U

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Tests for the mean of high-dimensional data

Dietmar Ferger

A bootstrap test based on the scaled squared norm of the sample mean yields valid level-alpha inference for high-dimensional means without sparsity or covariance structure assumptions.

arxiv:2605.16033 v1 · 2026-05-15 · math.ST · stat.TH

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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

The resulting bootstrap test yields asymptotic level-α procedures without requiring sparsity assumptions or structural conditions on the covariance matrix.

C2weakest assumption

The observations can be embedded into the Hilbert space l2 and a new Central Limit Theorem in l2 applies to establish the asymptotic distributional results for both fixed and increasing dimension.

C3one line summary

Bootstrap test for high-dimensional mean using squared-norm statistic V_n with asymptotic level-alpha validity via l2 embedding and a new CLT, without sparsity or covariance structure assumptions.

References

19 extracted · 19 resolved · 1 Pith anchors

[1] A. Araujo and E. Gin´ e,The Central Limit Theorem for Real and Banach Valued Random Variables, New York: John Wiley & Sons, 1980 1980

[2] Z. Bai and H. Saranadasa,Effect of high dimension: by an example of a two sample problem, Statist. Sinica6(1996), 311–329 1996

[3] Billingsley,Convergence of Probability Measures, New York: John Wiley & Sons, 1968 1968

[4] T. T. Cai, W. Liu and Y. Xia,Two-sample test of high dimensional means under dependence, J. R. Statist. Soc. B76Part 2 (2014), 349–372 2014

[5] A. Chakraborty and P. Chaudhuri,Tests for high-dimensional data based on means, spatial signs and spatial ranks, Ann. Statist.45(2) (2017), 771–799 2017

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:50.039733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca2c28735b3ebfe72effb32c8f3aabd526fdb8f141153575c1cab03f9a18f2ab

Aliases

arxiv: 2605.16033 · arxiv_version: 2605.16033v1 · doi: 10.48550/arxiv.2605.16033 · pith_short_12: ZIWCQ423H276 · pith_short_16: ZIWCQ423H276OLX7 · pith_short_8: ZIWCQ423

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/ZIWCQ423H276OLX7WMWI6OVL2U \
  | 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: ca2c28735b3ebfe72effb32c8f3aabd526fdb8f141153575c1cab03f9a18f2ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d689f7636b81000072e83c29e3130d801b28a093a27da72229a9ad33a2d4308d",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-15T15:08:05Z",
    "title_canon_sha256": "7b8e594e0c291c3cf0c647cfa3b16e14717fcd36d37e8a150018de89ba9dd1ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16033",
    "kind": "arxiv",
    "version": 1
  }
}