Jack W. Silverstein

collaborators

3 papers

math.PR2023

Exact Separation of Eigenvalues of Large Dimensional Noncentral Sample Covariance Matrices

Zhidong Bai, Jiang Hu, Jack W. Silverstein +1

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…

math.PR2023

No Eigenvalues Outside the Support of the Limiting Spectral Distribution of Large Dimensional noncentral Sample Covariance Matrices

Zhidong Bai, Jiang Hu, Jack W. Silverstein +1

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 variable…

math.PR2021

Limiting Eigenvalue Behavior of a Class of Large Dimensional Random Matrices Formed From a Hadamard Product

Jack W. Silverstein

This paper investigates the strong limiting behavior of the eigenvalues of the class of matrices $\frac{1}{N} (D_{n} \circ X_{n}) (D_{n} \circ X_{n})^{*}$ , studied in Girko 2001. Here, $X_n=(x_{ij})…