This paper discusses the problem of identifying a linear system from the frequency data when the measurements of the input and the output signals are both disturbed with noise. A typical example of such a problem is the identification of a system in a feedback loop. It is known that this problem can be solved using errors-in-varaibles methods if the covariance matrices of the disturbing noise (on input and output measurements) are a priori known. It is shown that the exact covariance matrices can be replaced by the sample covariance matrices : the system can be identified from the sample means and sample covariance matrices calculated from a (small) number M of independently repeated experiments. It is shown that under these conditions the estimates are still strongly consistent for an increasing number of data points N in each experiment (N-->infinity) if M greater than or equal to 4. The loss in efficiency is quantified (M greater than or equal to 6), and the expected value of the cost function (M greater than or equal to 4) and its variance (M greater than or equal to 6) are calculated.