A subspace estimator for fixed rank perturbations of large random matrices

Bai, 1999, Methodologies in spectral analysis of large-dimensional random matrices, a review, Statist. Sinica, 9, 611 Bai, 2004, CLT for linear spectral statistics of large-dimensional sample covariance matrices, Ann. Probab., 32, 553, 10.1214/aop/1078415845 Bai, 2008, Central limit theorems for eigenvalues in a spiked population model, Ann. Inst. H. Poincaré Probab. Statist., 44, 447, 10.1214/07-AIHP118 Baik, 2005, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, Ann. Probab., 33, 1643, 10.1214/009117905000000233 Baik, 2006, Eigenvalues of large sample covariance matrices of spiked population models, J. Multivariate Anal., 97, 1382, 10.1016/j.jmva.2005.08.003 F. Benaych-Georges, A. Guionnet, M. Maïda, Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, January 2010. Arxiv Preprint arXiv:1009.0145. F. Benaych-Georges, R.R. Nadakuditi, The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices (v1), October 2009. ArXiv e-prints. Benaych-Georges, 2011, The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices, Adv. Math., 10.1016/j.aim.2011.02.007 F. Benaych-Georges, R.R. Nadakuditi, The singular values and vectors of low rank perturbations of large rectangular random matrices, March 2011. ArXiv e-prints. Bianchi, 2011, Performance of statistical tests for single-source detection using random matrix theory, IEEE Trans. Inform. Theory, 57, 2400, 10.1109/TIT.2011.2111710 G. Bienvenu, L. Kopp, Adaptivity to background noise spatial coherence for high resolution passive methods, in: IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, ICASSP’80, vol. 5, April 1980, pp. 307–310. M. Capitaine, C. Donati-Martin, D. Féral, Central limit theorems for eigenvalues of deformations of Wigner matrices, March 2009. Arxiv Preprint arXiv:0903.4740. Capitaine, 2009, The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations, Ann. Probab., 37, 1, 10.1214/08-AOP394 Ciblat, 2002, Asymptotic analysis of blind cyclic correlation-based symbol-rate estimators, IEEE Trans. Inform. Theory, 48, 1922, 10.1109/TIT.2002.1013133 Geman, 1980, A limit theorem for the norm of random matrices, Ann. Probab., 8, 252, 10.1214/aop/1176994775 Hannan, 1971, Non-linear time series regression, J. Appl. Probab., 8, 767, 10.1017/S0021900200114664 Hannan, 1973, The estimation of frequency, J. Appl. Probab., 10, 510, 10.1017/S002190020011839X Hiai, 2000, vol. 77 Horn, 2007 Johnstone, 2001, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist., 29, 295, 10.1214/aos/1009210544 Marčenko, 1967, Distribution of eigenvalues in certain sets of random matrices, Mat. Sb. (NS), 72, 507 Nadler, 2011, On the distribution of the ratio of the largest eigenvalue to the trace of a Wishart matrix, J. Multivariate Anal., 102, 363, 10.1016/j.jmva.2010.10.005 Pastur, 2011, vol. 171 Pastur, 2007, On the law of addition of random matrices: covariance and the central limit theorem for traces of resolvent, vol. 42, 399 Paul, 2007, Asymptotics of sample eigenstructure for a large dimensional spiked covariance model, Statist. Sinica, 17, 1617 Péché, 2006, The largest eigenvalue of small rank perturbations of Hermitian random matrices, Probab. Theory Related Fields, 134, 127, 10.1007/s00440-005-0466-z Schmidt, 1986, Multiple emitter location and signal parameter estimation, IEEE Trans. Antennas and Propagation, 34, 276, 10.1109/TAP.1986.1143830 Stoica, 1989, MUSIC, maximum likelihood, and Cramer–Rao bound, IEEE Trans. Acoust. Speech Signal Process., 37, 720, 10.1109/29.17564