Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T19:17:28.713897Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T19:17:28.713897Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-10T08:16:58.503519Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-10T08:26:59.075053Z
82 of 82 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation f231bd08-c238-48af-a1e2-48a467171b1a · outbound
Testing Separability of High-Dimensional Covariance Matrices Allen and Robert Tibshirani
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d4bf1dcf-c740-4a79-bf00-ff7453dac421 · outbound
Testing Separability of High-Dimensional Covariance Matrices Wiley, 2003
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9bdfdb2e-a5ee-47a8-802d-f9fc6d0404d4 · outbound
Testing Separability of High-Dimensional Covariance Matrices Artin.The Gamma Function
Reference 3
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.
Observation 628b600e-5578-4958-83b6-95e5ba4d2a41 · outbound
Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work
Reference 4
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.
Observation 7cb40a8e-f536-4eb4-9605-c1f2f2c36694 · outbound
Testing Separability of High-Dimensional Covariance Matrices Silverstein.Spectral Analysis of Large Dimensional Random Matri- ces
Reference 5
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.
Observation 3f262ee0-60cc-4786-bea0-20062d0a914f · outbound
Testing Separability of High-Dimensional Covariance Matrices On sample eigenvalues in a generalized spiked population model.J
Reference 6
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.
Observation 50e60af8-f696-4fd6-84c3-d722362fdb2f · outbound
Testing Separability of High-Dimensional Covariance Matrices Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices.Ann
Reference 7
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.
Observation 30bab792-df9f-477f-bf7c-12bf8b6e2555 · outbound
Testing Separability of High-Dimensional Covariance Matrices Silverstein
Reference 8
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.
Observation 7b5212ea-c970-4fde-9b17-df95c0f2075a · outbound
Testing Separability of High-Dimensional Covariance Matrices Universality for the largest eigenvalue of sample covariance matrices with general population.Ann
Reference 9
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.
Observation 4ceb7754-5098-48ab-9972-113d18b6e110 · outbound
Testing Separability of High-Dimensional Covariance Matrices Tony Cai, Xiao Han, and Guangming Pan
Reference 10
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.
Observation 77501397-35d9-427d-9bf3-20dad89b46e1 · outbound
Testing Separability of High-Dimensional Covariance Matrices Chen and G.M
Reference 11
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.
Observation fd02e43b-b2d9-486d-807b-250865881565 · outbound
Testing Separability of High-Dimensional Covariance Matrices Testing separability of space–time functional processes.Biometrika, 104(2):425–437, 2017
Reference 12
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.
Observation 54b0c188-9751-415a-bff8-2d80d4eb24d9 · outbound
Testing Separability of High-Dimensional Covariance Matrices Maximum likelihood estimation for matrix normal models via quiver representations.SIAM J
Reference 13
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.
Observation 34beeb09-f7a8-4ad2-9c9b-0a8ccf4258a7 · outbound
Testing Separability of High-Dimensional Covariance Matrices Maximum likelihood estimation for tensor normal models via castling transforms.Forum math
Reference 14
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.
Observation 5b6ad7fe-301d-425d-a41d-c581d151053a · outbound
Testing Separability of High-Dimensional Covariance Matrices Diaconis and D
Reference 15
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.
Observation 11eab10e-cb65-45d0-8fa3-d61b002c7f1c · outbound
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
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.
Observation f249b9f7-0c1c-4cfb-a309-0e3d16bbf1d4 · outbound
Testing Separability of High-Dimensional Covariance Matrices Rational maximum likelihood estimators of kronecker covariance matrices.Algebr
Reference 17
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.
Observation 3815f22f-501d-4b33-8b6b-8eaefbeb06c4 · outbound
Testing Separability of High-Dimensional Covariance Matrices Existence and uniqueness of the kronecker covariance mle.Ann
Reference 18
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.
Observation 80ab8170-51cb-48dd-b75a-c6da28a55d75 · outbound
Testing Separability of High-Dimensional Covariance Matrices The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case.J
Reference 19
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.
Observation 84bd6a7a-f9db-45a9-acc6-05d41e00185d · outbound
Testing Separability of High-Dimensional Covariance Matrices Fisher, Xiaoqian Sun, and Colin M
Reference 20
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.
Observation a47f2cc4-68f5-46f0-85be-e082d2bdcd4e · outbound
Testing Separability of High-Dimensional Covariance Matrices Near optimal sample complexity for matrix and tensor normal models via geodesic convexity.Ann
Reference 21
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.
Observation 92ed97a2-f19d-4590-9ce3-04de9c615e9d · outbound
Testing Separability of High-Dimensional Covariance Matrices near optimal sample complexity for matrix and tensor normal models via geodesic convexity
Reference 22
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.
Observation 1ea13adf-4464-4982-9da7-f2ad04011233 · outbound
Testing Separability of High-Dimensional Covariance Matrices A higher-order lq decomposition for separable covariance models
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9f6f5e3e-553b-4c21-8506-cb121601231e · outbound
Testing Separability of High-Dimensional Covariance Matrices Testing the first- order separability hypothesis for spatio-temporal point patterns.Comput
Reference 24
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.
Observation c0b5d64b-f6e2-4bce-b630-93ba458ddb01 · outbound
Testing Separability of High-Dimensional Covariance Matrices Nonseparable, stationary covariance functions for space–time data.J
Reference 25
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.
Observation a1f2240e-0c0b-43d5-b0ac-06c0a249970d · outbound
Testing Separability of High-Dimensional Covariance Matrices Genton, and Peter Guttorp
Reference 26
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.
Observation 9442e6cf-e656-430d-8197-3404abaf7e9d · outbound
Testing Separability of High-Dimensional Covariance Matrices On the Rate of Convergence to the Marchenko--Pastur Distribution
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ac34ee52-fc8d-4f50-90e6-22f735b58573 · outbound
Testing Separability of High-Dimensional Covariance Matrices The tracy-widom law for the largest eigenvalue of f type matrix.Ann
Reference 28
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.
Observation 08bb59a6-063e-4253-b24c-c9cb53a6b19e · outbound
Testing Separability of High-Dimensional Covariance Matrices Asymptotic independence of point process and Frobenius norm of a large sample covariance matrix
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6a096f38-76a4-40ac-9498-95813ae5a17f · outbound
Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work
Reference 30
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.
Observation 6f1056ff-5c2b-4285-9dfc-5d6c83065d61 · outbound
Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work
Reference 31
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.
Observation 34e6b1c7-ba79-4ad7-ab40-0deb8ca998a0 · outbound
Testing Separability of High-Dimensional Covariance Matrices Testing stationarity of functional time series.J
Reference 32
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.
Observation 31031469-bd4a-41ac-a80b-f17d3cf39268 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1162c448-e3ff-4e97-98d7-f47408ca3aff · outbound
Testing Separability of High-Dimensional Covariance Matrices Partial generalized four moment theorem revisited.Bernoulli, 27(4):2337–2352, 2021
Reference 34
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.
Observation 7f9b5626-86fa-4900-8ae1-b6c469d3f3c6 · outbound
Testing Separability of High-Dimensional Covariance Matrices Spectral analysis of matrix scaling and operator scaling.SIAM J
Reference 35
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.
Observation 315f354e-6bd0-4fa6-823c-ec3b43ba92e0 · outbound
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
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.
Observation cc88edda-c181-40a4-a0ea-32111db7a8bb · outbound
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
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.
Observation f4ae12ae-31ac-4e6f-ab83-6fa74ebc7fdf · outbound
Testing Separability of High-Dimensional Covariance Matrices Lehmann and Joseph P
Reference 38
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.
Observation 59ab1bc9-429f-454f-8acc-8dce70477105 · outbound
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
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.
Observation 627ce2c7-ccce-4e80-843d-33aedaab0062 · outbound
Testing Separability of High-Dimensional Covariance Matrices Lindquist
Reference 40
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.
Observation 6117ce73-11c4-473a-a863-f431481acb3d · outbound
Testing Separability of High-Dimensional Covariance Matrices Linton and Haihan Tang
Reference 41
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.
Observation 8081bd2e-3f47-45eb-9ede-e8e784599644 · outbound
Testing Separability of High-Dimensional Covariance Matrices Van Loan
Reference 42
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.
Observation c4ac5c58-d79c-4e2d-9484-c087ae1fb620 · outbound
Testing Separability of High-Dimensional Covariance Matrices Zimmerman
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aede7d0e-1e2e-4546-8208-1e21e65690f5 · outbound
Testing Separability of High-Dimensional Covariance Matrices Manceur and Pierre Dutilleul
Reference 44
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.
Observation b53bbb89-ef87-4c99-b96d-d07e0db3acde · outbound
Testing Separability of High-Dimensional Covariance Matrices Manceur and Pierre Dutilleul
Reference 45
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.
Observation ec82b558-7a3b-4a66-8149-7d6e89aefe4c · outbound
Testing Separability of High-Dimensional Covariance Matrices The eigenvalue distribution in some ensembles of random matrices.Math
Reference 46
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.
Observation e6449867-8681-4b2d-a808-ee81959d3e20 · outbound
Testing Separability of High-Dimensional Covariance Matrices Panaretos
Reference 47
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.
Observation 944a602c-26a2-4342-8663-d1228ecacd03 · outbound
Testing Separability of High-Dimensional Covariance Matrices Panaretos
Reference 48
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.
Observation 564f68ac-e57f-4b17-a5a0-11cb268b8b2e · outbound
Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work
Reference 49
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.
Observation d6e90b53-4490-4e28-93fe-09f5d17e18a7 · outbound
Testing Separability of High-Dimensional Covariance Matrices Mitchell, Marc G
Reference 50
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.
Observation 13d8b1d4-f828-4e5b-8da0-a4ac617c2eac · outbound
Testing Separability of High-Dimensional Covariance Matrices A differential geometric approach to the geometric mean of symmetric positive-definite matrices.SIAM J
Reference 51
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.
Observation 305b5340-6dfe-4595-bf82-e28d051f1976 · outbound
Testing Separability of High-Dimensional Covariance Matrices Neudecker
Reference 52
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.
Observation b4c5a26b-7b95-49ea-8d2b-4c276c5565e8 · outbound
Testing Separability of High-Dimensional Covariance Matrices A riemannian framework for tensor computing.Int
Reference 53
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.
Observation 42d1d990-63ac-499b-8f53-0260f4cae5d5 · outbound
Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work
Reference 54
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.
Observation 2621bca8-c468-45d1-a756-79617d1aae5a · outbound
Testing Separability of High-Dimensional Covariance Matrices Dimension-free structured covariance estimation.Proc
Reference 55
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.
Observation 6b1fd28d-1ca5-4614-8a0c-18b6120b4cf3 · outbound
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
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.
Observation 29edaae3-fab2-453c-9528-fa988045f0d2 · outbound
Testing Separability of High-Dimensional Covariance Matrices de Mucnk, and Mathisca C.M
Reference 57
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.
Observation aee8909d-95d7-46b3-80eb-14ae1588bbb5 · outbound
Testing Separability of High-Dimensional Covariance Matrices Hanson-wright inequality and sub-gaussian concentra- tion.Electron
Reference 58
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.
Observation f0306a11-c657-412d-a153-fcda2858144c · outbound
Testing Separability of High-Dimensional Covariance Matrices Silverstein and Bai Z
Reference 59
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.
Observation 5c63d666-2ea7-4ac1-a28e-0a48bb3be2f9 · outbound
Testing Separability of High-Dimensional Covariance Matrices Simpson, Lloyd J
Reference 60
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.
Observation 976277be-40c1-4310-9ba1-f5caea3191f0 · outbound
Testing Separability of High-Dimensional Covariance Matrices A riemannian geometry of the multivariate normal model.Scand
Reference 61
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.
Observation 9ed3affd-48e6-4dfc-aa8e-6522b51c96a0 · outbound
Testing Separability of High-Dimensional Covariance Matrices Soloveychik and D
Reference 62
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.
Observation 35c72869-813c-4138-a598-aa00f84ff3ef · outbound
Testing Separability of High-Dimensional Covariance Matrices Covariance Estimation for Matrix-variate Data via Fixed-rank Core Covariance Geometry
Reference 63
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.
Observation 34fdaffb-1935-4cb9-8595-ed9e56fe3025 · outbound
Testing Separability of High-Dimensional Covariance Matrices R package version 1.1.0
Reference 64
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.
Observation 79ac156c-0529-42a4-9d0a-d89c22ec94f8 · outbound
Testing Separability of High-Dimensional Covariance Matrices Hero III, and Shuheng Zhou
Reference 65
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.
Observation 30958b77-9fc7-4491-9f6a-32aad42dbc0c · outbound
Testing Separability of High-Dimensional Covariance Matrices Hero III
Reference 66
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.
Observation 4defd6ca-2201-4918-9a4b-e4069e937135 · outbound
Testing Separability of High-Dimensional Covariance Matrices On the sphericity test with large-dimensional observations
Reference 67
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9dc82ffe-330e-4040-bdf8-15de17d2439a · outbound
Testing Separability of High-Dimensional Covariance Matrices High-dimensional sphericity test by extended likelihood ratio.Metrika, 84:1169—-1212, 2021
Reference 68
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.
Observation 85ce982f-3a70-457d-96ad-f92467114ecc · outbound
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
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.
Observation d4c37c32-b157-4da2-b015-ec972af8c92e · outbound
Testing Separability of High-Dimensional Covariance Matrices Springer, New York, 2nd edition, 2011
Reference 70
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.
Observation 2e8a89e8-7e67-4303-a3ea-8f6efeea527a · outbound
Testing Separability of High-Dimensional Covariance Matrices Positivity of matrices with generalized matrix functions.Acta Math
Reference 71
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.
Observation 65a47b8f-1004-4ea5-ac18-637c2d6f3066 · outbound
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
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.
Observation c3517ae7-1f32-478a-bd08-bcaaa2d2029d · outbound
Testing Separability of High-Dimensional Covariance Matrices Unresolved cited work
Reference 73
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.
Observation 2428910b-37bb-4e84-94dd-105b63fe2d87 · outbound
Testing Separability of High-Dimensional Covariance Matrices Hence,p 1 = 1 and similarly,p 2 = 1, wherer= 2
Reference 74
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.
Observation 15a83f0d-7439-4363-94a3-1048e72bfd0b · outbound
Testing Separability of High-Dimensional Covariance Matrices Thenp 2|p2 2−1 only whenp 2 = 1, which is a contradiction
Reference 75
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.
Observation 0ecac993-6a9f-4aa3-89d5-a7f3a30e90ac · outbound
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
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.
Observation 39447fd8-bef6-4110-a769-9403abe5d7f7 · outbound
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
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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 6c7c3dc2-dab1-4893-bdc9-3c65de058a86 · outbound
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
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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 0f61d3ae-8f6c-4ae4-99c1-406f9b8e6f5f · outbound
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
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.
Observation aa32e97f-c1ee-4eef-bc8e-c204367fce74 · outbound
Testing Separability of High-Dimensional Covariance Matrices Also, note thatλ 1(C)/λ= 1 +c
Reference 80
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.
Observation 3ae26b02-c7f1-47ca-a30b-c3df51867b51 · outbound
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
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.
Observation afb4a7f6-69e3-4576-85a3-07804a784474 · outbound
Testing Separability of High-Dimensional Covariance Matrices Here (p 1,p 2,n) = (20,20,1600)
Reference 82
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.
Observation ad533737-0b6b-48da-8568-76bbbeda9387 · inbound
Testing Covariance Separability in High Dimensions Testing Separability of High-Dimensional Covariance Matrices
Reference 30
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.