This paper is devoted to a statistical performance analysis of blind estimation of bit error rates (BERs) of a bank of detectors, using empirical estimation algorithms that have appeared in the literature (by Dixit et al.). In particular, we prove that these blind estimators asymptotically (in the number of observed bits) achieve the accuracy obtained with perfect knowledge of the transmitted bits. We propose a maximum-likelihood solution which follows from the standard expectation-maximization (EM) algorithm, considered to be a reference algorithm. Finally, the optimal fusion rule is revisited and our theoretical results are compared to Monte Carlo simulations