On the efficiency of output-error estimators

In this correspondence we consider a system with rational transfer function from input to output where the transfer function has
p
parameters. It is proved in [1] that when the input is a sum of sinusoids and has a two-sided line spectrum consisting of
p
distinct frequencies, then the output-error estimator and the prediction-error estimator are equally efficient. This result, which is at first sight a surprising one, is given an intuitively pleasing proof in this correspondence. This proof is based on the algorithm of [2].