Zobrazeno 1 - 10
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pro vyhledávání: '"Silverstein, Jack W."'
Let $ \bbB_n =\frac{1}{n}(\bbR_n + \bbT^{1/2}_n \bbX_n)(\bbR_n + \bbT^{1/2}_n \bbX_n)^* $ where $ \bbX_n $ is a $ p \times n $ matrix with independent standardized random variables, $ \bbR_n $ is a $ p \times n $ non-random matrix, representing the i
Externí odkaz:
http://arxiv.org/abs/2308.03481
Let $ \bbB_n =\frac{1}{n}(\bbR_n + \bbT^{1/2}_n \bbX_n)(\bbR_n + \bbT^{1/2}_n \bbX_n)^* $, where $ \bbX_n $ is a $ p \times n $ matrix with independent standardized random variables, $ \bbR_n $ is a $ p \times n $ non-random matrix and $ \bbT_{n} $ i
Externí odkaz:
http://arxiv.org/abs/2303.12478
In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the "general information-plus-noise" type, as studied in [14]. Through the equation defining its Stieltjes transform, it is s
Externí odkaz:
http://arxiv.org/abs/2302.01711
Autor:
Silverstein, Jack W.
This paper investigates the strong limiting behavior of the eigenvalues of the class of matrices $\frac1N(D_n\circ X_n)(D_n\circ X_n)^*$, studied in Girko 2001. Here, $X_n=(x_{ij})$ is an $n\times N$ random matrix consisting of independent complex st
Externí odkaz:
http://arxiv.org/abs/2112.04617
Autor:
Silverstein, Jack W.
For each $n$, let $U_n$ be Haar distributed on the group of $n\times n$ unitary matrices. Let $\bfx_{n,1},\ldots,\bfx_{n,m} $ denote orthogonal nonrandom unit vectors in ${\Bbb C}^n$ and let $\text{\bf u}_{n,k}=(u_k^1,\ldots,u_k^n)^*=U^*\text{\bf x}_
Externí odkaz:
http://arxiv.org/abs/2012.12950
A common sparse linear regression formulation is the l1 regularized least squares, which is also known as least absolute shrinkage and selection operator (LASSO). Approximate message passing (AMP) has been proved to asymptotically achieve the LASSO s
Externí odkaz:
http://arxiv.org/abs/2007.09299
Autor:
Bryc, Wlodek, Silverstein, Jack W.
Publikováno v:
Random Matrices: Theory and Applications, Vol. 9, No. 4 (2020) 2050012 (32 pages)
We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It provides a dec
Externí odkaz:
http://arxiv.org/abs/1802.02960
Autor:
Bai, Zhidong, Silverstein, Jack W.
Publikováno v:
In Journal of Multivariate Analysis March 2022 188
Publikováno v:
Journal of Theoretical Probability; Jun2024, Vol. 37 Issue 2, p1199-1229, 31p
This article demonstrates that the robust scatter matrix estimator $\hat{C}_N\in {\mathbb C}^{N\times N}$ of a multivariate elliptical population $x_1,\ldots,x_n\in {\mathbb C}^N$ originally proposed by Maronna in 1976, and defined as the solution (w
Externí odkaz:
http://arxiv.org/abs/1311.7034