A likelihood ratio test for testing the equality of the ranks of two non-negative definite covariance matrices arising in the area of signal processing is derived. The asymptotic distribution of the test statistic follows a Chi-square distribution from the general theory of likelihood ratio test.
Bhandary, Madhusudan and Kundu, Debasis
"Test for the Equality of the Number of Signals,"
Journal of Modern Applied Statistical Methods: Vol. 8
, Article 21.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss2/21