Technical Report 2022-008

Analyzing the Parameter Bias when an Instrumental Variable Method is Used with Noise-Corrupted Data

Torsten Söderström and Umberto Soverini

October 2022

When an output error model is fitted to data with noise-corrupted inputs using a prediction error method, a bias occurs. It was previously shown that the bias is of order O(1/delta) for a small pole-zero separation delta. These notes examine the same problem when an instrumental variable model is fitted. A similar result is shown to hold for the instrumental variable case.

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