On some nonparametric methods for detection of the number of signals

A simpler, more elegant, and more flexible method for estimating the number of signals is proposed. Strong consistency is proved. Bounds for error probabilities are given. This method depends on choosing a function with a parameter r. The previous methods correspond to the case r = 1. It seems the larger the r, the faster the convergence. We can choose r as any positive integer, even ∞. Applications are discussed, including the coherent cases.