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Paper Citation Record · LEDGER

Testing Separability of High-Dimensional Covariance Matrices

As of 17 August 2026, this Paper Citation Record lists 82 of 82 outbound references and 1 inbound Pith citation observation for arXiv:2506.17463.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.17463 v4

Coverage vector

measured 82 of 82 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:17:28.713897Z

measured 83 of 83 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-10T08:16:58.503519Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-10T08:26:59.075053Z

Reference resolution

82 of 82 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f231bd08-c238-48af-a1e2-48a467171b1a · outbound

This paper cites Allen and Robert Tibshirani.

Testing Separability of High-Dimensional Covariance Matrices Allen and Robert Tibshirani

Reference 1

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation d4bf1dcf-c740-4a79-bf00-ff7453dac421 · outbound

This paper cites Wiley, 2003.

Testing Separability of High-Dimensional Covariance Matrices Wiley, 2003

Reference 2

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Observation 9bdfdb2e-a5ee-47a8-802d-f9fc6d0404d4 · outbound

This paper cites Artin.The Gamma Function.

Testing Separability of High-Dimensional Covariance Matrices Artin.The Gamma Function

Reference 3

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Observation 628b600e-5578-4958-83b6-95e5ba4d2a41 · outbound

This paper cites an unresolved cited work.

Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work

Reference 4

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Observation 7cb40a8e-f536-4eb4-9605-c1f2f2c36694 · outbound

This paper cites Silverstein.Spectral Analysis of Large Dimensional Random Matri- ces.

Testing Separability of High-Dimensional Covariance Matrices Silverstein.Spectral Analysis of Large Dimensional Random Matri- ces

Reference 5

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Observation 3f262ee0-60cc-4786-bea0-20062d0a914f · outbound

This paper cites On sample eigenvalues in a generalized spiked population model.J.

Testing Separability of High-Dimensional Covariance Matrices On sample eigenvalues in a generalized spiked population model.J

Reference 6

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Source-reported events for the cited work

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Observation 50e60af8-f696-4fd6-84c3-d722362fdb2f · outbound

This paper cites Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices.Ann.

Testing Separability of High-Dimensional Covariance Matrices Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices.Ann

Reference 7

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Source-reported events for the cited work

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Observation 30bab792-df9f-477f-bf7c-12bf8b6e2555 · outbound

This paper cites Silverstein.

Testing Separability of High-Dimensional Covariance Matrices Silverstein

Reference 8

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 7b5212ea-c970-4fde-9b17-df95c0f2075a · outbound

This paper cites Universality for the largest eigenvalue of sample covariance matrices with general population.Ann.

Testing Separability of High-Dimensional Covariance Matrices Universality for the largest eigenvalue of sample covariance matrices with general population.Ann

Reference 9

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 4ceb7754-5098-48ab-9972-113d18b6e110 · outbound

This paper cites Tony Cai, Xiao Han, and Guangming Pan.

Testing Separability of High-Dimensional Covariance Matrices Tony Cai, Xiao Han, and Guangming Pan

Reference 10

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Source-reported events for the cited work

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Observation 77501397-35d9-427d-9bf3-20dad89b46e1 · outbound

This paper cites Chen and G.M.

Testing Separability of High-Dimensional Covariance Matrices Chen and G.M

Reference 11

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Source-reported events for the cited work

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Observation fd02e43b-b2d9-486d-807b-250865881565 · outbound

This paper cites Testing separability of space–time functional processes.Biometrika, 104(2):425–437, 2017.

Testing Separability of High-Dimensional Covariance Matrices Testing separability of space–time functional processes.Biometrika, 104(2):425–437, 2017

Reference 12

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 54b0c188-9751-415a-bff8-2d80d4eb24d9 · outbound

This paper cites Maximum likelihood estimation for matrix normal models via quiver representations.SIAM J.

Testing Separability of High-Dimensional Covariance Matrices Maximum likelihood estimation for matrix normal models via quiver representations.SIAM J

Reference 13

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Source-reported events for the cited work

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Observation 34beeb09-f7a8-4ad2-9c9b-0a8ccf4258a7 · outbound

This paper cites Maximum likelihood estimation for tensor normal models via castling transforms.Forum math.

Testing Separability of High-Dimensional Covariance Matrices Maximum likelihood estimation for tensor normal models via castling transforms.Forum math

Reference 14

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Observation 5b6ad7fe-301d-425d-a41d-c581d151053a · outbound

This paper cites Diaconis and D.

Testing Separability of High-Dimensional Covariance Matrices Diaconis and D

Reference 15

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 11eab10e-cb65-45d0-8fa3-d61b002c7f1c · outbound

This paper cites Some sphericity tests for high dimensional data based on ratio of the traces of sample covariance matrices.Stat.

Testing Separability of High-Dimensional Covariance Matrices Some sphericity tests for high dimensional data based on ratio of the traces of sample covariance matrices.Stat

Reference 16

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f249b9f7-0c1c-4cfb-a309-0e3d16bbf1d4 · outbound

This paper cites Rational maximum likelihood estimators of kronecker covariance matrices.Algebr.

Testing Separability of High-Dimensional Covariance Matrices Rational maximum likelihood estimators of kronecker covariance matrices.Algebr

Reference 17

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Observation 3815f22f-501d-4b33-8b6b-8eaefbeb06c4 · outbound

This paper cites Existence and uniqueness of the kronecker covariance mle.Ann.

Testing Separability of High-Dimensional Covariance Matrices Existence and uniqueness of the kronecker covariance mle.Ann

Reference 18

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 80ab8170-51cb-48dd-b75a-c6da28a55d75 · outbound

This paper cites The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case.J.

Testing Separability of High-Dimensional Covariance Matrices The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case.J

Reference 19

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 84bd6a7a-f9db-45a9-acc6-05d41e00185d · outbound

This paper cites Fisher, Xiaoqian Sun, and Colin M.

Testing Separability of High-Dimensional Covariance Matrices Fisher, Xiaoqian Sun, and Colin M

Reference 20

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation a47f2cc4-68f5-46f0-85be-e082d2bdcd4e · outbound

This paper cites Near optimal sample complexity for matrix and tensor normal models via geodesic convexity.Ann.

Testing Separability of High-Dimensional Covariance Matrices Near optimal sample complexity for matrix and tensor normal models via geodesic convexity.Ann

Reference 21

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 92ed97a2-f19d-4590-9ce3-04de9c615e9d · outbound

This paper cites near optimal sample complexity for matrix and tensor normal models via geodesic convexity.

Testing Separability of High-Dimensional Covariance Matrices near optimal sample complexity for matrix and tensor normal models via geodesic convexity

Reference 22

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 1ea13adf-4464-4982-9da7-f2ad04011233 · outbound

This paper cites A higher-order lq decomposition for separable covariance models.

Testing Separability of High-Dimensional Covariance Matrices A higher-order lq decomposition for separable covariance models

Reference 23

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:17:28.456861Z digest=sha256:31880462eae2861898c7af281d6132dab624e005d44c90ff4a3e852480af197d

Observation 9f6f5e3e-553b-4c21-8506-cb121601231e · outbound

This paper cites Testing the first- order separability hypothesis for spatio-temporal point patterns.Comput.

Testing Separability of High-Dimensional Covariance Matrices Testing the first- order separability hypothesis for spatio-temporal point patterns.Comput

Reference 24

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation c0b5d64b-f6e2-4bce-b630-93ba458ddb01 · outbound

This paper cites Nonseparable, stationary covariance functions for space–time data.J.

Testing Separability of High-Dimensional Covariance Matrices Nonseparable, stationary covariance functions for space–time data.J

Reference 25

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation a1f2240e-0c0b-43d5-b0ac-06c0a249970d · outbound

This paper cites Genton, and Peter Guttorp.

Testing Separability of High-Dimensional Covariance Matrices Genton, and Peter Guttorp

Reference 26

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 9442e6cf-e656-430d-8197-3404abaf7e9d · outbound

This paper cites On the Rate of Convergence to the Marchenko--Pastur Distribution.

Testing Separability of High-Dimensional Covariance Matrices On the Rate of Convergence to the Marchenko--Pastur Distribution

Reference 27

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:17:28.473695Z digest=sha256:07a9a6db5b9440eda513e84081c0aa112654c3fe53c386594f271ca10f22bd6c

Observation ac34ee52-fc8d-4f50-90e6-22f735b58573 · outbound

This paper cites The tracy-widom law for the largest eigenvalue of f type matrix.Ann.

Testing Separability of High-Dimensional Covariance Matrices The tracy-widom law for the largest eigenvalue of f type matrix.Ann

Reference 28

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 08bb59a6-063e-4253-b24c-c9cb53a6b19e · outbound

This paper cites Asymptotic independence of point process and Frobenius norm of a large sample covariance matrix.

Testing Separability of High-Dimensional Covariance Matrices Asymptotic independence of point process and Frobenius norm of a large sample covariance matrix

Reference 29

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:17:28.481795Z digest=sha256:60c575670a517b80c96422aace6ab6da35e65d3aaa8cacef8721f4463886c55d

Observation 6a096f38-76a4-40ac-9498-95813ae5a17f · outbound

This paper cites an unresolved cited work.

Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work

Reference 30

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Observation 6f1056ff-5c2b-4285-9dfc-5d6c83065d61 · outbound

This paper cites an unresolved cited work.

Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work

Reference 31

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Observation 34e6b1c7-ba79-4ad7-ab40-0deb8ca998a0 · outbound

This paper cites Testing stationarity of functional time series.J.

Testing Separability of High-Dimensional Covariance Matrices Testing stationarity of functional time series.J

Reference 32

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 31031469-bd4a-41ac-a80b-f17d3cf39268 · outbound

This paper cites Generalized four moment theorem and an application to clt for spiked eigenvalues of high-dimensional covariance matrices.Bernoulli, 27(1):274–294, 2021.

Testing Separability of High-Dimensional Covariance Matrices Generalized four moment theorem and an application to clt for spiked eigenvalues of high-dimensional covariance matrices.Bernoulli, 27(1):274–294, 2021

Reference 33

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no resolver link, observed 2026-08-15T19:17:28.500323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:17:28.500323Z digest=sha256:9e14acbab7584968ae24afef796f57f64b082ef72ef884ed756244c4e92fe569

Observation 1162c448-e3ff-4e97-98d7-f47408ca3aff · outbound

This paper cites Partial generalized four moment theorem revisited.Bernoulli, 27(4):2337–2352, 2021.

Testing Separability of High-Dimensional Covariance Matrices Partial generalized four moment theorem revisited.Bernoulli, 27(4):2337–2352, 2021

Reference 34

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 7f9b5626-86fa-4900-8ae1-b6c469d3f3c6 · outbound

This paper cites Spectral analysis of matrix scaling and operator scaling.SIAM J.

Testing Separability of High-Dimensional Covariance Matrices Spectral analysis of matrix scaling and operator scaling.SIAM J

Reference 35

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.509323Z digest=sha256:996a494136214a79fb90531748e7cfc94235d9d016e5a37ec47ff86bd94e56f5

Observation 315f354e-6bd0-4fa6-823c-ec3b43ba92e0 · outbound

This paper cites Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size.Ann.

Testing Separability of High-Dimensional Covariance Matrices Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size.Ann

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.497872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.513235Z digest=sha256:1aa8443514c68d150274e2fd0b3ace5447bdedd60b5dbbd60564a63d91a851b1

Observation cc88edda-c181-40a4-a0ea-32111db7a8bb · outbound

This paper cites Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population.Ann.

Testing Separability of High-Dimensional Covariance Matrices Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population.Ann

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.484886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.517394Z digest=sha256:fe53f9ccc516b80c94162602878be1d1f3ef19803c2f618184b97b992e02eb7a

Observation f4ae12ae-31ac-4e6f-ab83-6fa74ebc7fdf · outbound

This paper cites Lehmann and Joseph P.

Testing Separability of High-Dimensional Covariance Matrices Lehmann and Joseph P

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.469835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.522318Z digest=sha256:1b83439279ad06b4a9a8bfbde61bfd23f6b8b223d0326989886cc96eee6e3c52

Observation 59ab1bc9-429f-454f-8acc-8dce70477105 · outbound

This paper cites Testing the sphericity of a covariance matrix when the dimension is much larger than the sample size.Electron.

Testing Separability of High-Dimensional Covariance Matrices Testing the sphericity of a covariance matrix when the dimension is much larger than the sample size.Electron

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.454987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.526574Z digest=sha256:e460cfeb7d673c62a8c13373dbdd1459bcdea3fc8ed6c603eadaa3b98f1b3f7c

Observation 627ce2c7-ccce-4e80-843d-33aedaab0062 · outbound

This paper cites Lindquist.

Testing Separability of High-Dimensional Covariance Matrices Lindquist

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.440175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.530643Z digest=sha256:0c3fa9c81d19c8be5948be797d5e41b861c6aa07311d41771da7adce2feeb8b5

Observation 6117ce73-11c4-473a-a863-f431481acb3d · outbound

This paper cites Linton and Haihan Tang.

Testing Separability of High-Dimensional Covariance Matrices Linton and Haihan Tang

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.426470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.534500Z digest=sha256:e98a242d5ac5941a485e4061573a3ee6284305d79f99e14f5859bc3b6d28c8f8

Observation 8081bd2e-3f47-45eb-9ede-e8e784599644 · outbound

This paper cites Van Loan.

Testing Separability of High-Dimensional Covariance Matrices Van Loan

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.413114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.539330Z digest=sha256:8c32617f86dbfb2bd9f76e8219ff811bd8b6c6786962bd14a586244de727a747

Observation c4ac5c58-d79c-4e2d-9484-c087ae1fb620 · outbound

This paper cites Zimmerman.

Testing Separability of High-Dimensional Covariance Matrices Zimmerman

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-15T19:17:28.544368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:17:28.544368Z digest=sha256:e51620ed4dc50af90eb30d3cdbb4973f0f58fbe0589f1fbb675a4e77e10113e2

Observation aede7d0e-1e2e-4546-8208-1e21e65690f5 · outbound

This paper cites Manceur and Pierre Dutilleul.

Testing Separability of High-Dimensional Covariance Matrices Manceur and Pierre Dutilleul

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.391436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.548396Z digest=sha256:181c42c15cf43e890043d567ccb887cd43ec5da9a250a9c41cf028a1539d4582

Observation b53bbb89-ef87-4c99-b96d-d07e0db3acde · outbound

This paper cites Manceur and Pierre Dutilleul.

Testing Separability of High-Dimensional Covariance Matrices Manceur and Pierre Dutilleul

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.378986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.552885Z digest=sha256:cb4ba4ce702591d5d2b26bc5c20f25576e67984f96caeb4e4c1a816ff4a84bc8

Observation ec82b558-7a3b-4a66-8149-7d6e89aefe4c · outbound

This paper cites The eigenvalue distribution in some ensembles of random matrices.Math.

Testing Separability of High-Dimensional Covariance Matrices The eigenvalue distribution in some ensembles of random matrices.Math

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.365949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.557647Z digest=sha256:a72a31c58c125fbe316f9c62dd2dfc5a44a139256e776cb1bd4c439a2a2c9f7d

Observation e6449867-8681-4b2d-a808-ee81959d3e20 · outbound

This paper cites Panaretos.

Testing Separability of High-Dimensional Covariance Matrices Panaretos

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.352773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.561409Z digest=sha256:9ce56f07f3f674ad61098d3b148c53f0004bd231150dbcaa61396ac807f45a4b

Observation 944a602c-26a2-4342-8663-d1228ecacd03 · outbound

This paper cites Panaretos.

Testing Separability of High-Dimensional Covariance Matrices Panaretos

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.340308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.565893Z digest=sha256:546e18b43ea3b0efab5d96105f457240228adf1f9a5ddb22ffe6965ce284e78f

Observation 564f68ac-e57f-4b17-a5a0-11cb268b8b2e · outbound

This paper cites an unresolved cited work.

Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:17:29.327534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.570068Z digest=sha256:f4c9cb85458a1c55f55cabc8ee0f62bf4ec1af7aa02543b8cb633dd5730f98e7

Observation d6e90b53-4490-4e28-93fe-09f5d17e18a7 · outbound

This paper cites Mitchell, Marc G.

Testing Separability of High-Dimensional Covariance Matrices Mitchell, Marc G

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.314295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.573941Z digest=sha256:d82288f85300b8c78f1d88c9b5adf80ccdab4bf4708b3903114ba0757ef73d9c

Observation 13d8b1d4-f828-4e5b-8da0-a4ac617c2eac · outbound

This paper cites A differential geometric approach to the geometric mean of symmetric positive-definite matrices.SIAM J.

Testing Separability of High-Dimensional Covariance Matrices A differential geometric approach to the geometric mean of symmetric positive-definite matrices.SIAM J

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.301544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.578247Z digest=sha256:bdcd013cb756720b1bf941fcbadb69a0c2c596aa7e02cb21c261f1bc806729c4

Observation 305b5340-6dfe-4595-bf82-e28d051f1976 · outbound

This paper cites Neudecker.

Testing Separability of High-Dimensional Covariance Matrices Neudecker

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.287452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.582084Z digest=sha256:08754777d6f2f431cac4fee0aa475ed6830aea0eda88496b8c4f0a190a37ed49

Observation b4c5a26b-7b95-49ea-8d2b-4c276c5565e8 · outbound

This paper cites A riemannian framework for tensor computing.Int.

Testing Separability of High-Dimensional Covariance Matrices A riemannian framework for tensor computing.Int

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.274457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.585869Z digest=sha256:7347ec017cfb8455fbfe5aa72a156df5da06c6a5adec2aef05ba449fb7d0cf41

Observation 42d1d990-63ac-499b-8f53-0260f4cae5d5 · outbound

This paper cites an unresolved cited work.

Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:17:29.260300Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.589722Z digest=sha256:21296f3b7b6b726cf447e44c9737ad72e844c177c8f7c83e14fc3df9235b0c94

Observation 2621bca8-c468-45d1-a756-79617d1aae5a · outbound

This paper cites Dimension-free structured covariance estimation.Proc.

Testing Separability of High-Dimensional Covariance Matrices Dimension-free structured covariance estimation.Proc

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.245946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.593891Z digest=sha256:2fd59137fa84e0af0aa689902bb978b66e17518ce8e9b423f93ca0553ef4685b

Observation 6b1fd28d-1ca5-4614-8a0c-18b6120b4cf3 · outbound

This paper cites Asymptotic normality for eigenvalue statistics of a general sample covariance matrix whenp/n→∞and applications.Ann.

Testing Separability of High-Dimensional Covariance Matrices Asymptotic normality for eigenvalue statistics of a general sample covariance matrix whenp/n→∞and applications.Ann

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.232300Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.598590Z digest=sha256:8c7b2b13986f1f6cd6f239ca397d34a74895a2849f9b45cb44b6056f4caba27a

Observation 29edaae3-fab2-453c-9528-fa988045f0d2 · outbound

This paper cites de Mucnk, and Mathisca C.M.

Testing Separability of High-Dimensional Covariance Matrices de Mucnk, and Mathisca C.M

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.217633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.603412Z digest=sha256:07626a7dcec458a82ab2bb0c09070846790a7e8ba79d3197881b9e1bb4077b07

Observation aee8909d-95d7-46b3-80eb-14ae1588bbb5 · outbound

This paper cites Hanson-wright inequality and sub-gaussian concentra- tion.Electron.

Testing Separability of High-Dimensional Covariance Matrices Hanson-wright inequality and sub-gaussian concentra- tion.Electron

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.203398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.607424Z digest=sha256:5ccd31b0f1064b764ee773dece6b2918576cff226c25e070c6351a52af3141e1

Observation f0306a11-c657-412d-a153-fcda2858144c · outbound

This paper cites Silverstein and Bai Z.

Testing Separability of High-Dimensional Covariance Matrices Silverstein and Bai Z

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.189703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.611593Z digest=sha256:fddc9a03542e378209816c3aa6cbb7d0f9c86669dc4e754664d3b7038d0c5e11

Observation 5c63d666-2ea7-4ac1-a28e-0a48bb3be2f9 · outbound

This paper cites Simpson, Lloyd J.

Testing Separability of High-Dimensional Covariance Matrices Simpson, Lloyd J

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.175236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.615636Z digest=sha256:c5a97e1bd469d972aa7538c6c3c50056d8651b0947ad11714804e8971fa7b635

Observation 976277be-40c1-4310-9ba1-f5caea3191f0 · outbound

This paper cites A riemannian geometry of the multivariate normal model.Scand.

Testing Separability of High-Dimensional Covariance Matrices A riemannian geometry of the multivariate normal model.Scand

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.160602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.619675Z digest=sha256:07c07127730e8f2d1c204055a7728cb6cb7e1923399563608390a5a9092667d2

Observation 9ed3affd-48e6-4dfc-aa8e-6522b51c96a0 · outbound

This paper cites Soloveychik and D.

Testing Separability of High-Dimensional Covariance Matrices Soloveychik and D

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.147245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.623655Z digest=sha256:7bf41b12a994ee56072162ce19b9f856240258009345363aefc0d0316e4d86b1

Observation 35c72869-813c-4138-a598-aa00f84ff3ef · outbound

This paper cites Covariance Estimation for Matrix-variate Data via Fixed-rank Core Covariance Geometry.

Testing Separability of High-Dimensional Covariance Matrices Covariance Estimation for Matrix-variate Data via Fixed-rank Core Covariance Geometry

Reference 63

Resolution
verified exact
local_arxiv, observed 2026-08-15T19:17:28.862406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.628475Z digest=sha256:fc3388507d8757f92a29cd9a01765aa679c7442a9b7d17e667c93d411dd6422d

Observation 34fdaffb-1935-4cb9-8595-ed9e56fe3025 · outbound

This paper cites R package version 1.1.0.

Testing Separability of High-Dimensional Covariance Matrices R package version 1.1.0

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.134351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.633060Z digest=sha256:3e671b8f1149acd4a68f3b512f309fc1fbcfe6c5d30ca4a8d4c1076601362885

Observation 79ac156c-0529-42a4-9d0a-d89c22ec94f8 · outbound

This paper cites Hero III, and Shuheng Zhou.

Testing Separability of High-Dimensional Covariance Matrices Hero III, and Shuheng Zhou

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.120717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.637871Z digest=sha256:756c1ee906c60996526b181a5cd722ffd16f0f909507a16db297ab77f381c26d

Observation 30958b77-9fc7-4491-9f6a-32aad42dbc0c · outbound

This paper cites Hero III.

Testing Separability of High-Dimensional Covariance Matrices Hero III

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.107106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.642305Z digest=sha256:dcc1576af5c3c21c64452606ee91479df1380f925b554b3c3658e7053df64e62

Observation 4defd6ca-2201-4918-9a4b-e4069e937135 · outbound

This paper cites On the sphericity test with large-dimensional observations.

Testing Separability of High-Dimensional Covariance Matrices On the sphericity test with large-dimensional observations

Reference 67

Resolution
unresolved
no resolver link, observed 2026-08-15T19:17:28.646175Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:17:28.646175Z digest=sha256:1f735ff8e7dbd0c36ec6d9feedbc03dfd325a2ee6a0f1b38fd7703db7398e0b4

Observation 9dc82ffe-330e-4040-bdf8-15de17d2439a · outbound

This paper cites High-dimensional sphericity test by extended likelihood ratio.Metrika, 84:1169—-1212, 2021.

Testing Separability of High-Dimensional Covariance Matrices High-dimensional sphericity test by extended likelihood ratio.Metrika, 84:1169—-1212, 2021

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.083929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.649928Z digest=sha256:0ee5c2704207c61d242c52efbc22d75c1dc5968bb7ce5f1a3e19629e22d148f2

Observation 85ce982f-3a70-457d-96ad-f92467114ecc · outbound

This paper cites Testing kronecker product covariance matrices for high-dimensional matrix-variate data.Biometrika, 110(3):799––814, 2023.

Testing Separability of High-Dimensional Covariance Matrices Testing kronecker product covariance matrices for high-dimensional matrix-variate data.Biometrika, 110(3):799––814, 2023

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.070929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.653910Z digest=sha256:469881971565436c82a55ad78ba3ffea3564c27bf55737d1e505757295c9fd90

Observation d4c37c32-b157-4da2-b015-ec972af8c92e · outbound

This paper cites Springer, New York, 2nd edition, 2011.

Testing Separability of High-Dimensional Covariance Matrices Springer, New York, 2nd edition, 2011

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.057176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.657847Z digest=sha256:e8658672bc830b107e1987870fe5bd8e76a6b7417c13436343653969af0501cf

Observation 2e8a89e8-7e67-4303-a3ea-8f6efeea527a · outbound

This paper cites Positivity of matrices with generalized matrix functions.Acta Math.

Testing Separability of High-Dimensional Covariance Matrices Positivity of matrices with generalized matrix functions.Acta Math

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.043974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.662434Z digest=sha256:f9de0cdfcb930fc323d995b3ed0ead9331c04336b0e303a68e144a40c68997db

Observation 65a47b8f-1004-4ea5-ac18-637c2d6f3066 · outbound

This paper cites 34 Proof of Proposition 4.As an analogy to the proof of Proposition 1, it suffices to show that the singular values ofR( ˆC) do not depend on the value ofK.

Testing Separability of High-Dimensional Covariance Matrices 34 Proof of Proposition 4.As an analogy to the proof of Proposition 1, it suffices to show that the singular values ofR( ˆC) do not depend on the value ofK

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.030351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.666790Z digest=sha256:417d3db2440908a1b4a4b8bb5f8f9d0f83481569243cd3990a7dafb7bd0cffa8

Observation c3517ae7-1f32-478a-bd08-bcaaa2d2029d · outbound

This paper cites an unresolved cited work.

Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work

Reference 73

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:17:29.017020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.671563Z digest=sha256:5aaa284c3b3a8022ad4d25e53ff1055a2fa62274bdc9e378f85c9cb5505a108f

Observation 2428910b-37bb-4e84-94dd-105b63fe2d87 · outbound

This paper cites Hence,p 1 = 1 and similarly,p 2 = 1, wherer= 2.

Testing Separability of High-Dimensional Covariance Matrices Hence,p 1 = 1 and similarly,p 2 = 1, wherer= 2

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:29.002703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.675849Z digest=sha256:c3c1369389c409c445159bc828b70d01b6f5721fc338b00430d211a3a54e9315

Observation 15a83f0d-7439-4363-94a3-1048e72bfd0b · outbound

This paper cites Thenp 2|p2 2−1 only whenp 2 = 1, which is a contradiction.

Testing Separability of High-Dimensional Covariance Matrices Thenp 2|p2 2−1 only whenp 2 = 1, which is a contradiction

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:28.988667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.680551Z digest=sha256:1410aab7e2233693c5037febee3065e0719f4e80e252b18a374184ec21332332

Observation 0ecac993-6a9f-4aa3-89d5-a7f3a30e90ac · outbound

This paper cites •(p 1,p 2,r) = (p 2r,p 2,r): Recall from the proof of Theorem 1, ifOis partitioned as [O 1,...,O r], where each block hasp 2 columns,A i =√p2Oi.

Testing Separability of High-Dimensional Covariance Matrices •(p 1,p 2,r) = (p 2r,p 2,r): Recall from the proof of Theorem 1, ifOis partitioned as [O 1,...,O r], where each block hasp 2 columns,A i =√p2Oi

Reference 76

Resolution
malformed identifier
raw_fallback, observed 2026-08-15T19:17:28.974686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.685573Z digest=sha256:bf90e6bc2d3640cef7c304cb92b853b5996f3e150d1fdada6306cd5622d60106

Observation 39447fd8-bef6-4110-a769-9403abe5d7f7 · outbound

This paper cites Since|| ˜K−1−Ip||2 =O p(an) by (A4), Lemma A.19 withQ=I p implies that ˆE+ =E + +O(an) given ˜K.

Testing Separability of High-Dimensional Covariance Matrices Since|| ˜K−1−Ip||2 =O p(an) by (A4), Lemma A.19 withQ=I p implies that ˆE+ =E + +O(an) given ˜K

Reference 77

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:28.959048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.691665Z digest=sha256:04f113ee278fd2f2eff65e268a9cbdba77d782cb235e2af788ed3a778519bbb6

Observation 6c7c3dc2-dab1-4893-bdc9-3c65de058a86 · outbound

This paper cites For the consistency ofϕ 2 1, denote the event that|| ˜K−I p||2 =O(a n) byE n.Then by the law of iterated expectation, βn(ϕ2.

Testing Separability of High-Dimensional Covariance Matrices For the consistency ofϕ 2 1, denote the event that|| ˜K−I p||2 =O(a n) byE n.Then by the law of iterated expectation, βn(ϕ2

Reference 78

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:28.945453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.696563Z digest=sha256:d2b0faf6007985dea8ce01c835d3156c36969b249c8b2b1913415447378e93fb

Observation 0f61d3ae-8f6c-4ae4-99c1-406f9b8e6f5f · outbound

This paper cites Hence, the claim is proved ifP I,C (ϕ1 1(Y) = 1,E n| ˜K) converges to 1 by the dominated convergence theorem.

Testing Separability of High-Dimensional Covariance Matrices Hence, the claim is proved ifP I,C (ϕ1 1(Y) = 1,E n| ˜K) converges to 1 by the dominated convergence theorem

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:28.931903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.701035Z digest=sha256:51e18ddd8a59a0c84234e33da9f5084770503f953ad6a2791e71495cb68e025f

Observation aa32e97f-c1ee-4eef-bc8e-c204367fce74 · outbound

This paper cites Also, note thatλ 1(C)/λ= 1 +c.

Testing Separability of High-Dimensional Covariance Matrices Also, note thatλ 1(C)/λ= 1 +c

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:28.917812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.705410Z digest=sha256:f1574cd122d0b5deef77c6806bcadddd6610ddc000d7e3aa12a7dcf8d99721b2

Observation 3ae26b02-c7f1-47ca-a30b-c3df51867b51 · outbound

This paper cites We examine whether the above result holds when Σ is a core covariance matrix with a rank−r partial isotropic structure, focusing onr= 1,2.

Testing Separability of High-Dimensional Covariance Matrices We examine whether the above result holds when Σ is a core covariance matrix with a rank−r partial isotropic structure, focusing onr= 1,2

Reference 81

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:17:28.904335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.709864Z digest=sha256:67edc806c951a60c9657d66752ee5935d5d69b4a96ce0ba94fe35afaadcf9b69

Observation afb4a7f6-69e3-4576-85a3-07804a784474 · outbound

This paper cites Here (p 1,p 2,n) = (20,20,1600).

Testing Separability of High-Dimensional Covariance Matrices Here (p 1,p 2,n) = (20,20,1600)

Reference 82

Resolution
verified exact
raw_fallback, observed 2026-08-15T19:17:28.842661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:17:28.713897Z digest=sha256:aa66607ae6da3f2cc3993dd741e56deef86f1d31c38b29583775fe24c6469b53

Pith citing papers

Observation ad533737-0b6b-48da-8568-76bbbeda9387 · inbound

Testing Covariance Separability in High Dimensions cites this paper.

Testing Covariance Separability in High Dimensions Testing Separability of High-Dimensional Covariance Matrices

Reference 30

Resolution
verified exact
local_arxiv, observed 2026-07-10T08:26:59.076450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=arxiv_source observed=2026-07-10T08:16:58.503519Z digest=sha256:3743317bfb4999254fc41de78aa7c75fef3e6f402d604bfc7ab5b91978862fe6