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pith:HSZWC7SF

pith:2025:HSZWC7SFXPQPION3KVG5EWHQUL

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Multiple Testing of One-Sided Hypotheses with Conservative $p$-values

Hyungwon Choi, Jaesik Jeong, Johan Lim, Kwangok Seo

Estimating the marginal null distribution via empirical Bayes produces refined p-values that plug directly into standard multiple testing procedures for one-sided hypotheses.

arxiv:2512.24588 v2 · 2025-12-31 · stat.ME

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Claims

C1strongest claim

we estimate the marginal null distribution of the test statistics within an empirical Bayes framework and construct refined p-values based on this estimated distribution. These refined p-values can then be directly used in standard multiple testing procedures without modification.

C2weakest assumption

The marginal null distribution of the test statistics can be accurately estimated from the observed data using empirical Bayes, under the maintained assumption that test statistics are normal with unit variance.

C3one line summary

Estimating the marginal null distribution via empirical Bayes produces refined p-values that restore power in one-sided multiple testing when conventional p-values are conservative due to negative null means.

References

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[1] Azzalini, A. (1985). A class of distributions which includes the normal ones.Scandinavian Journal of Statistics 12(2), 171–178 1985

[2] Barber, R. F. and E. J. Cand` es (2019). A knockoff filter for high-dimensional selective inference 2019

[3] Benjamini, Y. and Y. Hochberg (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing.Journal of the Royal statistical society: series B (Method- ological) 1995

[4] Brent, R. P. (2013).Algorithms for minimization without derivatives. Courier Corporation 2013

[5] de U˜ na-´Alvarez, J. (2023). Controlling the number of significant effects in multiple testing. arXiv preprint arXiv:2311.00885 2023

Receipt and verification

First computed	2026-05-17T23:39:16.753938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3cb3617e45bbe0f439bb554dd258f0a2f91f64e1f3e524976c1f7ada16d25ab4

Aliases

arxiv: 2512.24588 · arxiv_version: 2512.24588v2 · doi: 10.48550/arxiv.2512.24588 · pith_short_12: HSZWC7SFXPQP · pith_short_16: HSZWC7SFXPQPION3 · pith_short_8: HSZWC7SF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HSZWC7SFXPQPION3KVG5EWHQUL \
  | 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: 3cb3617e45bbe0f439bb554dd258f0a2f91f64e1f3e524976c1f7ada16d25ab4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "955acaa37dcd5c31841e23e15739f43f65d73fc21c9a3913976a5f9c03e55841",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2025-12-31T03:26:43Z",
    "title_canon_sha256": "3328280da44c344d0bfd6bca9c9e75c9e9b6ef229db4436a8c7ef1b348b2133b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.24588",
    "kind": "arxiv",
    "version": 2
  }
}