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This paper shows that a certain class of estimates of invariants of (over)parameterized models are with probability one independent of the particular (over)parameterization chosen. The result is nonasymptotic, and the estimators considered minimize a cost function that is invariant with respect to the same parameter transformation as the overparameterized model. Index Terms - Identification, (over)parameterized models.

It is the common conviction that frequency domain system identification suffers from the drawback that it cannot handle arbitrary signals without introducing systematic errors. This paper shows that it is possible to deal with nonperiodic signals without any approximation and under the same assumptions as in the time domain, by estimating simultaneously some initial conditions and the system model parameters. Index Terms - Frequency domain identification, parametric transfer function models.