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In a parallel distributed detection system each local detector makes a decision based on its own observations and transmits its local decision to a fusion center, where a global decision is made. Given fixed local decision rules, in order to design the optimal fusion rule, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probabilities of the hypotheses. Such knowledge is not available in most practical cases. We propose a blind technique for the M-ary distributed detection problem. The occurrence number of a possible decision combination at all local detectors is multinomially distributed with the occurrence probability being a nonlinear function of the prior probabilities of hypotheses and the parameters describing the performance of local detectors. We derive least squares (LS) and maximum likelihood (ML) estimates of unknown parameters using local decisions and compare their individual performance. We also derive analytically the overall detection performance for both binary and M-ary distributed detection and discuss the difference of the overall detection performance obtained using the estimated values of unknown parameters and their true values. Finally, we demonstrate the applicability of our results through numerical examples.