L2 Model reduction and Variance Reduction - Extended Version

In this contribution we demonstrate that estimating a low order model (leaving some dynamics unmodeled) by L2 model reduction of a higher order estimated model may give smaller variance and mean square error than directly estimating it from the same data that produced the high order model. It will also be shown in a quite general case that the reduced model will reach the Cramer-Rao bound if no under modeling is present. From the derivations of this result it follows that L2model reduction is optimal, meaning that the reduced model possesses the lowest possible variance