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Eigenvalues of large sample covariance matrices of spiked population models

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Cited by:

  1. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
  2. Brendan P. W. Ames & Mingyi Hong, 2016. "Alternating direction method of multipliers for penalized zero-variance discriminant analysis," Computational Optimization and Applications, Springer, vol. 64(3), pages 725-754, July.
  3. Bo Zhang & Guangming Pan & Jiti Gao, 2016. "CLT for Largest Eigenvalues and Unit Root Tests for High-Dimensional Nonstationary Time Series," Monash Econometrics and Business Statistics Working Papers 11/16, Monash University, Department of Econometrics and Business Statistics.
  4. Bo Zhang & Jiti Gao & Guangming Pan & Yanrong Yang, 2023. "Eigen-Analysis for High-Dimensional Time Series Clustering," Monash Econometrics and Business Statistics Working Papers 22/23, Monash University, Department of Econometrics and Business Statistics.
  5. Wang, Zhendong & Xu, Xingzhong, 2021. "Testing high dimensional covariance matrices via posterior Bayes factor," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
  6. Yata, Kazuyoshi & Aoshima, Makoto, 2013. "PCA consistency for the power spiked model in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 334-354.
  7. Liu, Yan & Bai, Zhidong & Li, Hua & Hu, Jiang & Lv, Zhihui & Zheng, Shurong, 2022. "RDS free CLT for spiked eigenvalues of high-dimensional covariance matrices," Statistics & Probability Letters, Elsevier, vol. 187(C).
  8. Passemier, Damien & McKay, Matthew R. & Chen, Yang, 2015. "Hypergeometric functions of matrix arguments and linear statistics of multi-spiked Hermitian matrix models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 124-146.
  9. Hsiao, Cheng & Wan, Shui Ki, 2014. "Is there an optimal forecast combination?," Journal of Econometrics, Elsevier, vol. 178(P2), pages 294-309.
  10. Fleermann, Michael & Heiny, Johannes, 2023. "Large sample covariance matrices of Gaussian observations with uniform correlation decay," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 456-480.
  11. Patrick K. Kimes & Yufeng Liu & David Neil Hayes & James Stephen Marron, 2017. "Statistical significance for hierarchical clustering," Biometrics, The International Biometric Society, vol. 73(3), pages 811-821, September.
  12. Feher Kristen & Whelan James & Müller Samuel, 2012. "Exploring Multicollinearity Using a Random Matrix Theory Approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-35, May.
  13. Wang, Qinwen & Silverstein, Jack W. & Yao, Jian-feng, 2014. "A note on the CLT of the LSS for sample covariance matrix from a spiked population model," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 194-207.
  14. Yata, Kazuyoshi & Aoshima, Makoto, 2012. "Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 193-215.
  15. Kargin, Vladislav, 2015. "On estimation in the reduced-rank regression with a large number of responses and predictors," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 377-394.
  16. Passemier, Damien & Yao, Jianfeng, 2014. "Estimation of the number of spikes, possibly equal, in the high-dimensional case," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 173-183.
  17. Shen, Keren & Yao, Jianfeng & Li, Wai Keung, 2019. "On a spiked model for large volatility matrix estimation from noisy high-frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 207-221.
  18. Yata, Kazuyoshi & Aoshima, Makoto, 2013. "Correlation tests for high-dimensional data using extended cross-data-matrix methodology," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 313-331.
  19. Shabalin, Andrey A. & Nobel, Andrew B., 2013. "Reconstruction of a low-rank matrix in the presence of Gaussian noise," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 67-76.
  20. Bo Zhang & Jiti Gao & Guangming Pan, 2020. "Estimation and Testing for High-Dimensional Near Unit Root Time Series," Monash Econometrics and Business Statistics Working Papers 12/20, Monash University, Department of Econometrics and Business Statistics.
  21. Dey, Rounak & Lee, Seunggeun, 2019. "Asymptotic properties of principal component analysis and shrinkage-bias adjustment under the generalized spiked population model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 145-164.
  22. Edoardo Saccenti & Marieke E. Timmerman, 2017. "Considering Horn’s Parallel Analysis from a Random Matrix Theory Point of View," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 186-209, March.
  23. Anna Bykhovskaya & Vadim Gorin, 2023. "High-Dimensional Canonical Correlation Analysis," Papers 2306.16393, arXiv.org, revised Aug 2023.
  24. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
  25. Shu Wang & Jia-Ren Lin & Eduardo D Sontag & Peter K Sorger, 2019. "Inferring reaction network structure from single-cell, multiplex data, using toric systems theory," PLOS Computational Biology, Public Library of Science, vol. 15(12), pages 1-25, December.
  26. Joongyeub Yeo & George Papanicolaou, 2016. "Random matrix approach to estimation of high-dimensional factor models," Papers 1611.05571, arXiv.org, revised Nov 2017.
  27. Jung, Sungkyu & Sen, Arusharka & Marron, J.S., 2012. "Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 190-203.
  28. Peña, Daniel & Smucler, Ezequiel & Yohai, Victor J., 2021. "Sparse estimation of dynamic principal components for forecasting high-dimensional time series," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1498-1508.
  29. Xinyi Zhong & Chang Su & Zhou Fan, 2022. "Empirical Bayes PCA in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 853-878, July.
  30. Bolla, Marianna & Friedl, Katalin & Krámli, András, 2010. "Singular value decomposition of large random matrices (for two-way classification of microarrays)," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 434-446, February.
  31. Damien Passemier & Zhaoyuan Li & Jianfeng Yao, 2017. "On estimation of the noise variance in high dimensional probabilistic principal component analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 51-67, January.
  32. Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
  33. Romain Allez & Jean-Philippe Bouchaud, 2012. "Eigenvector dynamics: general theory and some applications," Papers 1203.6228, arXiv.org, revised Jul 2012.
  34. Lee, Myung Hee, 2012. "On the border of extreme and mild spiked models in the HDLSS framework," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 162-168.
  35. Nick Patterson & Alkes L Price & David Reich, 2006. "Population Structure and Eigenanalysis," PLOS Genetics, Public Library of Science, vol. 2(12), pages 1-20, December.
  36. Li, Weiming & Zhu, Junpeng, 2023. "CLT for spiked eigenvalues of a sample covariance matrix from high-dimensional Gaussian mean mixtures," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
  37. Bai, Zhidong & Yao, Jianfeng, 2012. "On sample eigenvalues in a generalized spiked population model," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 167-177.
  38. Maïda, M. & Najim, J. & Péché, S., 2007. "Large deviations for weighted empirical mean with outliers," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1373-1403, October.
  39. Dörnemann, Nina & Dette, Holger, 2023. "Fluctuations of the diagonal entries of a large sample precision matrix," Statistics & Probability Letters, Elsevier, vol. 198(C).
  40. Couillet, Romain & Pascal, Frédéric & Silverstein, Jack W., 2015. "The random matrix regime of Maronna’s M-estimator with elliptically distributed samples," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 56-78.
  41. Forzani, Liliana & Gieco, Antonella & Tolmasky, Carlos, 2017. "Likelihood ratio test for partial sphericity in high and ultra-high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 18-38.
  42. Feldman, Michael J., 2023. "Spiked singular values and vectors under extreme aspect ratios," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
  43. Hachem, Walid & Loubaton, Philippe & Mestre, Xavier & Najim, Jamal & Vallet, Pascal, 2013. "A subspace estimator for fixed rank perturbations of large random matrices," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 427-447.
  44. Weiming Li & Jianfeng Yao, 2015. "On generalized expectation-based estimation of a population spectral distribution from high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 359-373, April.
  45. Deo, Rohit S., 2016. "On the Tracy–Widom approximation of studentized extreme eigenvalues of Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 265-272.
  46. Mo, M.Y., 2010. "Universality in complex Wishart ensembles for general covariance matrices with 2 distinct eigenvalues," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1203-1225, May.
  47. Virta, Joni, 2021. "Testing for subsphericity when n and p are of different asymptotic order," Statistics & Probability Letters, Elsevier, vol. 179(C).
  48. Guerra Urzola, Rosember & Van Deun, Katrijn & Vera, J. C. & Sijtsma, K., 2021. "A guide for sparse PCA : Model comparison and applications," Other publications TiSEM 4d35b931-7f49-444b-b92f-a, Tilburg University, School of Economics and Management.
  49. Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
  50. Rosember Guerra-Urzola & Katrijn Van Deun & Juan C. Vera & Klaas Sijtsma, 2021. "A Guide for Sparse PCA: Model Comparison and Applications," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 893-919, December.
  51. Ding, Xiucai & Ji, Hong Chang, 2023. "Spiked multiplicative random matrices and principal components," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 25-60.
  52. Collins, Benoît & Matsumoto, Sho & Saad, Nadia, 2014. "Integration of invariant matrices and moments of inverses of Ginibre and Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 1-13.
  53. M. Capitaine, 2013. "Additive/Multiplicative Free Subordination Property and Limiting Eigenvectors of Spiked Additive Deformations of Wigner Matrices and Spiked Sample Covariance Matrices," Journal of Theoretical Probability, Springer, vol. 26(3), pages 595-648, September.
  54. Bo Zhang & Jiti Gao & Guangming Pan, 2019. "A Near Unit Root Test for High-Dimensional Nonstationary Time Series," Monash Econometrics and Business Statistics Working Papers 10/19, Monash University, Department of Econometrics and Business Statistics.
  55. Couillet, Romain, 2015. "Robust spiked random matrices and a robust G-MUSIC estimator," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 139-161.
  56. Yuyang Xu & Zhonghua Liu & Jianfeng Yao, 2023. "An eigenvalue ratio approach to inferring population structure from whole genome sequencing data," Biometrics, The International Biometric Society, vol. 79(2), pages 891-902, June.
  57. Liusha Yang & Matthew R. Mckay & Romain Couillet, 2018. "High-Dimensional MVDR Beamforming: Optimized Solutions Based on Spiked Random Matrix Models," Post-Print hal-01957672, HAL.
  58. Paul, Debashis & Silverstein, Jack W., 2009. "No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 37-57, January.
  59. Zeng, Yicheng & Zhu, Lixing, 2023. "Order determination for spiked-type models with a divergent number of spikes," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
  60. Yata, Kazuyoshi & Aoshima, Makoto, 2010. "Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2060-2077, October.
  61. Bai, Zhidong & Wang, Chen, 2015. "A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 333-340.
  62. Michael Bridges & Elizabeth A Heron & Colm O'Dushlaine & Ricardo Segurado & The International Schizophrenia Consortium (ISC) & Derek Morris & Aiden Corvin & Michael Gill & Carlos Pinto, 2011. "Genetic Classification of Populations Using Supervised Learning," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-12, May.
  63. Bo Zhang & Jiti Gao & Guangming Pan & Yanrong Yang, 2019. "Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices," Monash Econometrics and Business Statistics Working Papers 31/19, Monash University, Department of Econometrics and Business Statistics.
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