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Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices

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Cited by:

  1. Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.
  2. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2018. "Estimation of the global minimum variance portfolio in high dimensions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 371-390.
  3. Jin, Baisuo & Wang, Cheng & Miao, Baiqi & Lo Huang, Mong-Na, 2009. "Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2112-2125, October.
  4. Olivier Ledoit & Michael Wolf, 2019. "The power of (non-)linear shrinking: a review and guide to covariance matrix estimation," ECON - Working Papers 323, Department of Economics - University of Zurich, revised Feb 2020.
  5. Merlevède, F. & Peligrad, M., 2016. "On the empirical spectral distribution for matrices with long memory and independent rows," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2734-2760.
  6. Chen, Jiaqi & Zhang, Yangchun & Li, Weiming & Tian, Boping, 2018. "A supplement on CLT for LSS under a large dimensional generalized spiked covariance model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 57-65.
  7. G. Pan & J. Gao & Y. Yang & M. Guo, 2012. "Independence Test for High Dimensional Random Vectors," Monash Econometrics and Business Statistics Working Papers 1/12, Monash University, Department of Econometrics and Business Statistics.
  8. Xie, Junshan & Zeng, Yicheng & Zhu, Lixing, 2021. "Limiting laws for extreme eigenvalues of large-dimensional spiked Fisher matrices with a divergent number of spikes," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
  9. Olivier Ledoit & Sandrine P�ch�, 2009. "Eigenvectors of some large sample covariance matrices ensembles," IEW - Working Papers 407, Institute for Empirical Research in Economics - University of Zurich.
  10. Pavel Yaskov, 2018. "LLN for Quadratic Forms of Long Memory Time Series and Its Applications in Random Matrix Theory," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2032-2055, December.
  11. Li, Yuling & Zhou, Huanchao & Hu, Jiang, 2023. "The eigenvector LSD of information plus noise matrices and its application to linear regression model," Statistics & Probability Letters, Elsevier, vol. 197(C).
  12. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2016. "Spectral analysis of the Moore–Penrose inverse of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 160-172.
  13. Weiming Li, 2014. "Local expectations of the population spectral distribution of a high-dimensional covariance matrix," Statistical Papers, Springer, vol. 55(2), pages 563-573, May.
  14. Niu, Zhenzhen & Hu, Jiang & Bai, Zhidong & Gao, Wei, 2019. "On LR simultaneous test of high-dimensional mean vector and covariance matrix under non-normality," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 338-344.
  15. 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.
  16. Xinghua Zheng & Yingying Li, 2010. "On the estimation of integrated covariance matrices of high dimensional diffusion processes," Papers 1005.1862, arXiv.org, revised Mar 2012.
  17. Wen, Jun, 2018. "Estimation of two high-dimensional covariance matrices and the spectrum of their ratio," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 1-29.
  18. 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.
  19. Couillet, Romain & Kammoun, Abla & Pascal, Frédéric, 2016. "Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 249-274.
  20. Ledoit, Olivier & Wolf, Michael, 2017. "Numerical implementation of the QuEST function," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 199-223.
  21. Bai, Z.D. & Zhang, L.X., 2010. "The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1927-1949, October.
  22. Wang, Lili & Paul, Debashis, 2014. "Limiting spectral distribution of renormalized separable sample covariance matrices when p/n→0," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 25-52.
  23. Ningning Xia & Zhidong Bai, 2015. "Functional CLT of eigenvectors for large sample covariance matrices," Statistical Papers, Springer, vol. 56(1), pages 23-60, February.
  24. Jamshid Namdari & Debashis Paul & Lili Wang, 2021. "High-Dimensional Linear Models: A Random Matrix Perspective," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 645-695, August.
  25. Taras Bodnar & Stepan Mazur & Nestor Parolya, 2019. "Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix‐variate location mixture of normal distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 636-660, June.
  26. Dozier, R. Brent & Silverstein, Jack W., 2007. "Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1099-1122, July.
  27. Xiaoping Zhou & Dmitry Malioutov & Frank J. Fabozzi & Svetlozar T. Rachev, 2014. "Smooth monotone covariance for elliptical distributions and applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1555-1571, September.
  28. Hsu, Chih-Yuan & Wu, Tiee-Jian, 2013. "Efficient estimation of the mode of continuous multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 148-159.
  29. Ledoit, Olivier & Wolf, Michael, 2021. "Shrinkage estimation of large covariance matrices: Keep it simple, statistician?," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
  30. Olivier Ledoit & Michael Wolf, 2019. "Shrinkage estimation of large covariance matrices: keep it simple, statistician?," ECON - Working Papers 327, Department of Economics - University of Zurich, revised Jun 2021.
  31. Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
  32. Li, Hua & Bai, Zhi Dong & Wong, Wing Keung, 2015. "High dimensional Global Minimum Variance Portfolio," MPRA Paper 66284, University Library of Munich, Germany.
  33. Junshan Xie, 2013. "Limiting spectral distribution for a type of sample covariance matrices," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(5), pages 695-710, October.
  34. Huanchao Zhou & Zhidong Bai & Jiang Hu, 2023. "The Limiting Spectral Distribution of Large-Dimensional General Information-Plus-Noise-Type Matrices," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1203-1226, June.
  35. Claudio Heinrich & Mark Podolskij, 2014. "On spectral distribution of high dimensional covariation matrices," CREATES Research Papers 2014-54, Department of Economics and Business Economics, Aarhus University.
  36. Olivier Ledoit & Michael Wolf, 2017. "Analytical nonlinear shrinkage of large-dimensional covariance matrices," ECON - Working Papers 264, Department of Economics - University of Zurich, revised Nov 2018.
  37. Kei Nakagawa & Mitsuyoshi Imamura & Kenichi Yoshida, 2018. "Risk-Based Portfolios with Large Dynamic Covariance Matrices," IJFS, MDPI, vol. 6(2), pages 1-14, May.
  38. Taras Bodnar & Yarema Okhrin & Nestor Parolya, 2022. "Optimal Shrinkage-Based Portfolio Selection in High Dimensions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 140-156, December.
  39. Tingting Zou & Shurong Zheng & Zhidong Bai & Jianfeng Yao & Hongtu Zhu, 2022. "CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data," Statistical Papers, Springer, vol. 63(2), pages 605-664, April.
  40. Couillet, Romain & Tiomoko, Malik & Zozor, Steeve & Moisan, Eric, 2019. "Random matrix-improved estimation of covariance matrix distances," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
  41. Jean-Philippe Bouchaud & Laurent Laloux & M. Augusta Miceli & Marc Potters, 2005. "Large dimension forecasting models and random singular value spectra," Science & Finance (CFM) working paper archive 500066, Science & Finance, Capital Fund Management.
  42. Tsubasa Ito & Tatsuya Kubokawa, 2015. "Linear Ridge Estimator of High-Dimensional Precision Matrix Using Random Matrix Theory ," CIRJE F-Series CIRJE-F-995, CIRJE, Faculty of Economics, University of Tokyo.
  43. Li, Hua & Bai, Zhidong & Wong, Wing-Keung & McAleer, Michael, 2022. "Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization," Econometrics and Statistics, Elsevier, vol. 24(C), pages 133-150.
  44. 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.
  45. 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.
  46. 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.
  47. Wenjie Wang, 2012. "Bootstrapping Anderson-Rubin Statistic and J Statistic in Linear IV Models with Many Instruments," KIER Working Papers 810, Kyoto University, Institute of Economic Research.
  48. Li, Zeng & Pan, Guangming & Yao, Jianfeng, 2015. "On singular value distribution of large-dimensional autocovariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 119-140.
  49. Olivier Ledoit & Michael Wolf, 2019. "Quadratic shrinkage for large covariance matrices," ECON - Working Papers 335, Department of Economics - University of Zurich, revised Dec 2020.
  50. Wang, Cheng & Yang, Jing & Miao, Baiqi & Cao, Longbing, 2013. "Identity tests for high dimensional data using RMT," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 128-137.
  51. Zeng, Xingyuan, 2019. "Spectral distribution of large generalized random kernel matrices," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 100-110.
  52. Olivier Ledoit & Michael Wolf, 2013. "Optimal estimation of a large-dimensional covariance matrix under Stein’s loss," ECON - Working Papers 122, Department of Economics - University of Zurich, revised Mar 2017.
  53. Jiti Gao & Xiao Han & Guangming Pan & Yanrong Yang, 2014. "High Dimensional Correlation Matrices: CLT and Its Applications," Monash Econometrics and Business Statistics Working Papers 26/14, Monash University, Department of Econometrics and Business Statistics.
  54. Tian, Xintao & Lu, Yuting & Li, Weiming, 2015. "A robust test for sphericity of high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 217-227.
  55. Xu, Yangchang & Xia, Ningning, 2023. "On the eigenvectors of large-dimensional sample spatial sign covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
  56. Svensson, Jens, 2007. "The asymptotic spectrum of the EWMA covariance estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 621-630.
  57. Pan, Guangming, 2010. "Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1330-1338, July.
  58. Rubio, Francisco & Mestre, Xavier, 2011. "Spectral convergence for a general class of random matrices," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 592-602, May.
  59. Konstantin Glombek, 2014. "Statistical Inference for High-Dimensional Global Minimum Variance Portfolios," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 845-865, December.
  60. Marwa Banna & Florence Merlevède, 2015. "Limiting Spectral Distribution of Large Sample Covariance Matrices Associated with a Class of Stationary Processes," Journal of Theoretical Probability, Springer, vol. 28(2), pages 745-783, June.
  61. Guhlich, Matthias & Nagel, Jan & Dette, Holger, 2010. "Random block matrices generalizing the classical Jacobi and Laguerre ensembles," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1884-1897, September.
  62. 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.
  63. Couillet, Romain, 2015. "Robust spiked random matrices and a robust G-MUSIC estimator," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 139-161.
  64. Li, Weiming & Qin, Yingli, 2014. "Hypothesis testing for high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 108-119.
  65. Ledoit, Olivier & Wolf, Michael, 2015. "Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 360-384.
  66. Pan, Guangming & Miao, Boqi & Jin, Baisuo, 2005. "Some limiting theorems of some random quadratic forms," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 151-157, December.
  67. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
  68. Taras Bodnar & Arjun K. Gupta & Nestor Parolya, 2013. "Optimal Linear Shrinkage Estimator for Large Dimensional Precision Matrix," Papers 1308.0931, arXiv.org, revised Mar 2014.
  69. Zhang, Yangchun & Hu, Jiang & Li, Weiming, 2022. "CLT for linear spectral statistics of high-dimensional sample covariance matrices in elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
  70. Péché, S., 2006. "Non-white Wishart ensembles," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 874-894, April.
  71. Gao, Jiti & Pan, Guangming & Yang, Yanrong, 2012. "Testing Independence for a Large Number of High–Dimensional Random Vectors," MPRA Paper 45073, University Library of Munich, Germany, revised 15 Mar 2013.
  72. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.
  73. Dozier, R. Brent & Silverstein, Jack W., 2007. "On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 678-694, April.
  74. Bai, Z.D. & Miao, Baiqi & Jin, Baisuo, 2007. "On limit theorem for the eigenvalues of product of two random matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 76-101, January.
  75. 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.
  76. Ningning Xia & Zhidong Bai, 2019. "Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices," Statistical Papers, Springer, vol. 60(3), pages 983-1015, June.
  77. Yao, Jianfeng, 2012. "A note on a Marčenko–Pastur type theorem for time series," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 22-28.
  78. Guangming Pan & Jiti Gao & Yanrong Yang & Meihui Guo, 2015. "Cross-sectional Independence Test for a Class of Parametric Panel Data Models," Monash Econometrics and Business Statistics Working Papers 17/15, Monash University, Department of Econometrics and Business Statistics.
  79. Nathan Noiry, 2021. "Spectral Measures of Spiked Random Matrices," Journal of Theoretical Probability, Springer, vol. 34(2), pages 923-952, June.
  80. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2016. "Direct shrinkage estimation of large dimensional precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 223-236.
  81. Robert, Christian Y. & Rosenbaum, Mathieu, 2010. "On the limiting spectral distribution of the covariance matrices of time-lagged processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2434-2451, November.
  82. He, Yi & Jaidee, Sombut & Gao, Jiti, 2023. "Most powerful test against a sequence of high dimensional local alternatives," Journal of Econometrics, Elsevier, vol. 234(1), pages 151-177.
  83. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
  84. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2014. "On the strong convergence of the optimal linear shrinkage estimator for large dimensional covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 215-228.
  85. 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.
  86. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
  87. Yi He & Sombut Jaidee & Jiti Gao, 2020. "Most Powerful Test against High Dimensional Free Alternatives," Monash Econometrics and Business Statistics Working Papers 13/20, Monash University, Department of Econometrics and Business Statistics.
  88. 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.
  89. Jerzy Rydlewski & Małgorzata Snarska & Dominik Mielczarek & Daniel Kosiorowski, 2014. "Sparse Methods for Analysis of Sparse Multivariate Data From Big Economic Databases," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(1), pages 111-132, January.
  90. Yi†Hui Zhou & J. S. Marron & Fred A. Wright, 2018. "Eigenvalue significance testing for genetic association," Biometrics, The International Biometric Society, vol. 74(2), pages 439-447, June.
  91. Couillet, Romain & McKay, Matthew, 2014. "Large dimensional analysis and optimization of robust shrinkage covariance matrix estimators," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 99-120.
  92. 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).
  93. 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.
  94. Qian, Manling & Tao, Li & Li, Erqian & Tian, Maozai, 2020. "Hypothesis testing for the identity of high-dimensional covariance matrices," Statistics & Probability Letters, Elsevier, vol. 161(C).
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