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

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.