Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices

Authors:
R. Brent Dozier;Jack W. Silverstein
Affiliations:
North Carolina State University, Raleigh, NC 27695, USA;North Carolina State University, Raleigh, NC 27695, USA
Venue:
Journal of Multivariate Analysis
Year:
2007

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Abstract

A derivation of results on the analytic behavior of the limiting spectral distribution of sample covariance matrices of the ''information-plus-noise'' type, as studied in Dozier and Silverstein [On the empirical distribution of eigenvalues of large dimensional information-plus-noise type matrices, 2004, submitted for publication], is presented. It is shown that, away from zero, the limiting distribution possesses a continuous density. The density is analytic where it is positive and, for the most relevant cases of a in the boundary of its support, exhibits behavior closely resembling that of |x-a| for x near a. A procedure to determine its support is also analyzed.