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The problem of estimating the unknown parameters of linear discrete-time stochastic system models is considered for the case when the observations may contain noise alone. The interruptions in the observations are modeled as an independent stationary binary (zero or one) sequence where the probability of an interruption may not be known. The criterion for parameter estimation is chosen to be minimization of the prediction errors using linear predictors. Sufficient conditions for strong consistency of the parameter estimates are derived. It is shown by means of an example that even a few missing observations can lead to a serious degradation in the quality of the parameter estimate.