Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T11:31:17.387378Z
Paper Citation Record · LEDGER
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses
As of 18 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2504.15510.
A citation records a reference. It does not transfer a finding from one paper to another.
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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-14T11:15:04.329014Z
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Source: cited_works
Reference resolution
22 of 22 outbound references displayed
- verified exact0
- verified fuzzy18
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b8accb99-515a-45a0-86e7-b80be7999ae5 · outbound
This paper cites Isotropic local laws for sample covariance and generalized Wigner matrices.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Isotropic local laws for sample covariance and generalized Wigner matrices
Reference 1
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- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.743365Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7ffa41f6-6bd6-4fd1-acb2-cf9f83dcbc83 · outbound
This paper cites Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation
Reference 2
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- metadata mismatch
- local_arxiv, observed 2026-08-16T11:31:17.446444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5f0fcd88-8bdb-4112-8162-6e5c9e7a528b · outbound
This paper cites (3) There exists sufficiently small constants C ą 0 and C1ą 0 such that for all zPtE` iη : |E´ Θ1|ď C, 0ăηăC´1u inf τPSGλ |τ`qpzq|ě C1, whereSGλ is the support of Gλ.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses (3) There exists sufficiently small constants C ą 0 and C1ą 0 such that for all zPtE` iη : |E´ Θ1|ď C, 0ăηăC´1u inf τPSGλ |τ`qpzq|ě C1, whereSGλ is the support of Gλ
Reference 6
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- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.699763Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9f67c5a3-ae6a-42b8-838f-8d4cdde95644 · outbound
This paper cites Let zPD and suppose that |˜z´z|ď δpzq, where ˜z“´ 1{upzq` γ2ϕp´upzqq.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Let zPD and suppose that |˜z´z|ď δpzq, where ˜z“´ 1{upzq` γ2ϕp´upzqq
Reference 7
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- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.685543Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8fe15588-6bbc-47e1-bb9d-c399e900830d · outbound
This paper cites Let zPQ and suppose that |˜z´z|ď δpzq, where ˜z“vpzq` „ 1`γ2 ż τdF Σ8pτq ´τvpzq` λ ȷ´1.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Let zPQ and suppose that |˜z´z|ď δpzq, where ˜z“vpzq` „ 1`γ2 ż τdF Σ8pτq ´τvpzq` λ ȷ´1
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.670729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e9ffe472-2516-417c-a29f-8996929807ea · outbound
This paper cites (ii) The averaged local law in Qppq holds as ˆϕppzq´ ϕppzq“ Oă ˆ 1 n2η ˙ , where ˆϕppzq“ p´1trRpzq.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses (ii) The averaged local law in Qppq holds as ˆϕppzq´ ϕppzq“ Oă ˆ 1 n2η ˙ , where ˆϕppzq“ p´1trRpzq
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.656219Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2a69cd31-6ff5-4f46-853e-150bd689c340 · outbound
This paper cites We have }J}ď C η3, }BzJ}ď C η6.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses We have }J}ď C η3, }BzJ}ď C η6
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.643356Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ebd0f181-3941-457c-a9ba-d6219413812a · outbound
This paper cites an unresolved cited work.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:31:17.630059Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ebcb2337-7e4d-4aa5-b92e-fc4a6fac882f · outbound
This paper cites Let us first estimate Λ o.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Let us first estimate Λ o
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.616120Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b8f9fb46-9f96-4d89-adee-e2aef21b7f93 · outbound
This paper cites Applying Lemma S.4.6 or Corollary S.4.3, when ηě 1, |ˆϕp´ϕp|ď Cp|δ1|`| δ2|q ă ΨB ăn´1{2 2.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Applying Lemma S.4.6 or Corollary S.4.3, when ηě 1, |ˆϕp´ϕp|ď Cp|δ1|`| δ2|q ă ΨB ăn´1{2 2
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.601548Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4f600a91-8bb3-4b8e-9972-2529789cac6b · outbound
This paper cites Then on QppqYQppq away we have 1 p pÿ u“1 1 pλ{σu´z´ 1 n2 řp`n2 i“p`1 Jiiq2p1´ Euq 1 Juu “Oă ` Υ2˘ and 1 n2 p`n2ÿ i“p`1 p1´ Eiq 1 Jii “Oă ` Υ2˘.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Then on QppqYQppq away we have 1 p pÿ u“1 1 pλ{σu´z´ 1 n2 řp`n2 i“p`1 Jiiq2p1´ Euq 1 Juu “Oă ` Υ2˘ and 1 n2 p`n2ÿ i“p`1 p1´ Eiq 1 Jii “Oă ` Υ2˘
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.586418Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 850edf40-f6e9-449a-9464-caa1e20c1017 · outbound
This paper cites Therefore, to show ˇˇˇˇˇ 1 p pÿ j“1 fpℓjpGλqq´ ż fpτqdGλpτq ˇˇˇˇˇ ă 1 n2 , it suffices to show ¿ ˆR |fpzq| ˇˇˇˆϕppzq´ ϕppzq ˇˇˇdz ă 1 n2.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Therefore, to show ˇˇˇˇˇ 1 p pÿ j“1 fpℓjpGλqq´ ż fpτqdGλpτq ˇˇˇˇˇ ă 1 n2 , it suffices to show ¿ ˆR |fpzq| ˇˇˇˆϕppzq´ ϕppzq ˇˇˇdz ă 1 n2
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.570119Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1ef244ac-db55-4e06-9413-2cfd6ca01279 · outbound
This paper cites local laws.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses local laws
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.555080Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ebf4bad1-79d4-4be6-8149-a3606d1a58b8 · outbound
This paper cites Let ˆΘp1“ ˆfp´ ˆβpq and ˆΦpzq“ d ℑˆqppzq n1η ` 1 n1η.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Let ˆΘp1“ ˆfp´ ˆβpq and ˆΦpzq“ d ℑˆqppzq n1η ` 1 n1η
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.540696Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 04257bee-d96f-4f8f-8644-8ffaaacd0b84 · outbound
This paper cites Therefore, ´ˆqppzq is away from the support of Gλ.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Therefore, ´ˆqppzq is away from the support of Gλ
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.524282Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 245fbb02-55b7-4710-8dde-03c0f388bb33 · outbound
This paper cites an unresolved cited work.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:31:17.508341Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 52f07a72-df28-4b62-84d0-46fb168c377c · outbound
This paper cites 1 pνTD1{2pW2`λIpq´1D1{2ν`oPp1q. Using Lemma 2.7 of Bai and Silverstein (1998), conditional on W2, 1 pνTD1{2pW2`λIpq´1D1{2ν“ 1 ptr.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses 1 pνTD1{2pW2`λIpq´1D1{2ν`oPp1q. Using Lemma 2.7 of Bai and Silverstein (1998), conditional on W2, 1 pνTD1{2pW2`λIpq´1D1{2ν“ 1 ptr
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.494068Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 68f4c7e5-6870-4b31-a1af-22cfb74939a5 · outbound
This paper cites Therefore, s1pxq“ C pρ´xq2 `C ż τąρ dGλpτq τ´x Ñ8, as xÒρ.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Therefore, s1pxq“ C pρ´xq2 `C ż τąρ dGλpτq τ´x Ñ8, as xÒρ
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.478277Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation bad5e9c7-0701-4e4c-894c-212e964dbec7 · outbound
This paper cites Using Theorem 5.1 of Li (2024), there exists constants C1, C2 and ϵ such that C1 ?x´ρďfGλpxqď C2 ?x´ρ, x Ppρ,ρ `ϵq where fGλ is the density function of Gλ.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Using Theorem 5.1 of Li (2024), there exists constants C1, C2 and ϵ such that C1 ?x´ρďfGλpxqď C2 ?x´ρ, x Ppρ,ρ `ϵq where fGλ is the density function of Gλ
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.462892Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7791cb86-bae8-46c4-884d-beac592613f1 · outbound
This paper cites Pillai, N.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Pillai, N
Reference 197
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.728550Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d5137852-438b-4917-9d4b-4b8ead605d0f · outbound
This paper cites Ridge-regularized Largest Root Test for High-Dimensional General Linear Hypotheses.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Ridge-regularized Largest Root Test for High-Dimensional General Linear Hypotheses
Reference 1001
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:31:17.714233Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0968d010-c3d0-4921-bc51-8ac28e588165 · outbound
This paper cites Geometric sensitivity of random matrix results: consequences for shrinkage estimators of covariance and related statistical methods.
Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses Geometric sensitivity of random matrix results: consequences for shrinkage estimators of covariance and related statistical methods
Reference 2006
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:31:17.301713Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation c57e03ce-7d57-4395-83f2-86116cc2d6e1 · inbound
Adaptable Regularized CCA Tests for Independence of High-Dimensional Random Vectors cites this paper.
Adaptable Regularized CCA Tests for Independence of High-Dimensional Random Vectors Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses
Reference 144
- Resolution
- unresolved
- no resolver link, observed 2026-07-14T11:15:04.329014Z
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Unavailable: canonical work link unavailable.