# Estimating Population Eigenvalues From Large Dimensional Sample Covariance Matrices

Wednesday, September 28, 2011 - 3:00pm - 4:00pm

Keller 3-180

Jack Silverstein (North Carolina State University)

I will begin by reviewing limiting properties of the eigenvalues of a class of sample covariance matrices, where the vector dimension and the sample size

approach infinity, their ratio approaching a positive constant. These properties are relevant in situations in multivariate analysis where the vector dimension is large, but the number of samples needed to adequately approximate the population matrix (as prescribed in standard statistical procedures) cannot be attained. Work has been done in estimating the population eigenvalues from those of the sample covariance matrix. I will introduce a method devised by X. Mestre, and will present an extension of his method to another ensemble of random matrices important in wireless communications.

approach infinity, their ratio approaching a positive constant. These properties are relevant in situations in multivariate analysis where the vector dimension is large, but the number of samples needed to adequately approximate the population matrix (as prescribed in standard statistical procedures) cannot be attained. Work has been done in estimating the population eigenvalues from those of the sample covariance matrix. I will introduce a method devised by X. Mestre, and will present an extension of his method to another ensemble of random matrices important in wireless communications.

MSC Code:

62J10

Keywords: