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In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but theExpand
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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
SummaryIn this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tendExpand
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On detection of the number of signals in presence of white noise
In this paper, the authors propose procedures for detection of the number of signals in presence of Gaussian white noise under an additive model. This problem is related to the problem of finding theExpand
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On asymptotics of eigenvectors of large sample covariance matrix
Let {X ij }, i, j = ..., be a double array of i.i.d. complex random variables with EX 11 = 0, E|X 11 | 2 = 1 and E|X 11 | 4 <∞, and let An = (1 N T 1/2 n X n X* n (T 1/2 n , where T 1/2 n is theExpand
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Asymptotic distributions of the maximal depth estimators for regression and multivariate location
We derive the asymptotic distribution of the maximal depth regression estimator recently proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection-based depth and theExpand
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M-estimation of multivariate linear regression parameters under a convex discrepancy function
There is vast literature on M-estimation of linear regression parameters. Most of the papers deal with special cases by choosing particular discrepancy functions to be minimized or particularExpand
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Kernel estimators of density function of directional data
Let X be a unit vector random variable taking values on a k-dimensional sphere [Omega] with probability density function f(x). The problem considered is one of estimating f(x) based on n independentExpand
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A note on the largest eigenvalue of a large dimensional sample covariance matrix
Let {vij; i, J = 1, 2, ...} be a family of i.i.d. random variables with E(v114) = [infinity]. For positive integers p, n with p = p(n) and p/n --> y > 0 as n --> [infinity], let Mn = (1/n) Vn VnT ,Expand
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