On rates of convergence of general information criteria in signal processing when the noise covariance matrix is arbitrary

The authors give exponential-type bounds on the probabilities of detection error under certain conditions. The bounds tend to zero rapidly as the sample size increases. These procedures are referred to as general information criterion (GIC) procedures since each is consistent and, under certain conditions, the rate of convergence of the estimate of the number of signals to the true value is rapid. The authors give bounds on the probability of wrong detection of the GIC procedure when the noise variance is unknown. Upper bounds on the probabilities of detection error are also obtained