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We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy.
Rosenthal, Haskell P.H. P. (1970). On the subspaces of L p L^{p} ( p > 2 ) (p>2) spanned by sequences of independent random variables. Israel J. Math. 8 273–303
1970
Earlier work this paper cites.
Bai, Z. D.Z. D., Silverstein, Jack W.J. W. andYin, Y. Q.Y. Q. (1988). A note on the largest eigenvalue of a large-dimensional sample covariance matrix. J. Multivariate Anal. 26 166–168
1988
Earlier work this paper cites.
Bai, Z. D.Z. D. andYin, Y. Q.Y. Q. (1993). Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix. Ann. Probab. 21 1275–1294
1993
Earlier work this paper cites.
Figiel, T.T., Hitczenko, P.P., Johnson, W. B.W. B., Schechtman, G.G. andZinn, J.J. (1997). Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities. Trans. Amer. Math. Soc. 349 997–1027
1997
Earlier work this paper cites.
Kannan, RaviR., Lovász, LászlóL. andSimonovits, MiklósM. (1997). Random walks and an O ∗ ( n 5 ) O^{*}(n^{5}) volume algorithm for convex bodies. Random Structures Algorithms 11 1–50
1997
Earlier work this paper cites.
de la Peña, Víctor H.V. H. andGiné, EvaristE. (1999). Decoupling: From Dependence to Independence: Randomly Stopped Processes U U -Statistics and Processes Martingales and Beyond. Springer, New York
1999
Earlier work this paper cites.
Rudelson, M.M. (1999). Random vectors in the isotropic position. J. Funct. Anal. 164 60–72
1999
Cited alongside, same era.
Latala, RafalR. (2005). Some estimates of norms of random matrices. Proc. Amer. Math. Soc. 133 1273–1282 (electronic)
2005
Cited alongside, same era.
Paouris, G.G. (2006). Concentration of mass on convex bodies. Geom. Funct. Anal. 16 1021–1049
2006
Cited alongside, same era.
Adamczak, Rados λ
2010
Cited alongside, same era.
Srivastava, NikhilN. (2010). Spectral sparsification and restricted invertibility. Ph.D. thesis, Yale Univ
2010
Cited alongside, same era.
Adamczak, Rados λ
2011
Cited alongside, same era.
Benaych-Georges, FlorentF. andNadakuditi, Raj RaoR. R. (2011). The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Adv. Math. 227 494–521
2011
Closest in time.
Vershynin, R.R. (2011). A simple decoupling inequality in probability theory. Available at http://www-personal.umich.edu/~romanv/papers/decoupling- simple.pdf
2011
Closest in time.
Batson, Joshua D.J. D., Spielman, Daniel A.D. A. andSrivastava, NikhilN. (2012). Twice-Ramanujan sparsifiers. SIAM J. Comput. 41 1704–1721
2012
Closest in time.
Vershynin, R.R. (2012). How close is the sample covariance matrix to the actual covariance matrix? J. Theoret. Probab. 25 655–686
2012
Closest in time.
Vershynin, R.R. (2012). Introduction to the non-asymptotic analysis of random matrices. In Compressed Sensing
2012
Closest in time.
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