On the non-asymptotic concentration of heteroskedastic Wishart-type matrix
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[1] H. Weyl. Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung) , 1912 .
[2] Chandler Davis. The rotation of eigenvectors by a perturbation , 1963 .
[3] W. Kahan,et al. The Rotation of Eigenvectors by a Perturbation. III , 1970 .
[4] Z. Bai,et al. Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices , 1993 .
[5] C. Tracy,et al. Introduction to Random Matrices , 1992, hep-th/9210073.
[6] A. Syvänen. Accessing genetic variation: genotyping single nucleotide polymorphisms , 2001, Nature Reviews Genetics.
[7] D. Ruppert. The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .
[8] S. Boucheron,et al. Moment inequalities for functions of independent random variables , 2005, math/0503651.
[9] Zhidong Bai,et al. CONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES PART II: SAMPLE COVARIANCE MATRICES , 2008 .
[10] R. Vershynin. Spectral norm of products of random and deterministic matrices , 2008, 0812.2432.
[11] Harrison H. Zhou,et al. Optimal rates of convergence for covariance matrix estimation , 2010, 1010.3866.
[12] Roman Vershynin,et al. Introduction to the non-asymptotic analysis of random matrices , 2010, Compressed Sensing.
[13] Rebecca Willett,et al. Poisson Noise Reduction with Non-local PCA , 2012, Journal of Mathematical Imaging and Vision.
[14] T. Tao. Topics in Random Matrix Theory , 2012 .
[15] J. Salmon,et al. Poisson noise reduction with non-local PCA , 2012, ICASSP.
[16] Raj Rao Nadakuditi,et al. The singular values and vectors of low rank perturbations of large rectangular random matrices , 2011, J. Multivar. Anal..
[17] Andrew B. Nobel,et al. Reconstruction of a low-rank matrix in the presence of Gaussian noise , 2010, J. Multivar. Anal..
[18] Gábor Lugosi,et al. Concentration Inequalities - A Nonasymptotic Theory of Independence , 2013, Concentration Inequalities.
[19] V. Koltchinskii,et al. Concentration inequalities and moment bounds for sample covariance operators , 2014, 1405.2468.
[20] D. Donoho,et al. Minimax risk of matrix denoising by singular value thresholding , 2013, 1304.2085.
[21] A. Bandeira,et al. Sharp nonasymptotic bounds on the norm of random matrices with independent entries , 2014, 1408.6185.
[22] Universality for general Wigner-type matrices , 2015, 1506.05098.
[23] M. Lelarge,et al. Reconstruction in the Labelled Stochastic Block Model , 2015, IEEE Transactions on Network Science and Engineering.
[24] Anru R. Zhang,et al. Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics , 2016, 1605.00353.
[25] J. Tropp. The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach , 2015, 1506.04711.
[26] Will Perkins,et al. Spectral thresholds in the bipartite stochastic block model , 2015, COLT.
[27] Necdet Batır. Bounds for the Gamma Function , 2017, 1705.06167.
[28] Devavrat Shah,et al. Rank Centrality: Ranking from Pairwise Comparisons , 2012, Oper. Res..
[29] R. Handel. On the spectral norm of Gaussian random matrices , 2015, 1502.05003.
[30] Lydia T. Liu,et al. $e$PCA: High dimensional exponential family PCA , 2016, The Annals of Applied Statistics.
[31] Pierre Del Moral,et al. An Introduction to Wishart Matrix Moments , 2017, Found. Trends Mach. Learn..
[32] Ke Wang,et al. Singular vector and singular subspace distribution for the matrix denoising model , 2018, 1809.10476.
[33] Arun K. Kuchibhotla,et al. Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression , 2018, 1804.02605.
[34] R. Latala,et al. The dimension-free structure of nonhomogeneous random matrices , 2017, Inventiones mathematicae.
[35] Jeffrey A. Fessler,et al. Asymptotic performance of PCA for high-dimensional heteroscedastic data , 2017, J. Multivar. Anal..
[36] S. Girard,et al. Sub‐Weibull distributions: Generalizing sub‐Gaussian and sub‐Exponential properties to heavier tailed distributions , 2019, Stat.
[37] Anru R. Zhang,et al. On the non‐asymptotic and sharp lower tail bounds of random variables , 2018, Stat.
[38] Anru R. Zhang,et al. Heteroskedastic PCA: Algorithm, optimality, and applications , 2018, The Annals of Statistics.