document: L/sub 2 / model reduction and variance reduction We examine certain variance properties of model reduction . The focus is on L/sub 2 / model reduction , but some general results are also presented . These general results can be used to analyze various other model reduction schemes . The models we study are finite impulse response -LRB- FIR -RRB- and output error -LRB- OE -RRB- models . We compare the variance of two estimated models . The first one is estimated directly from data and the other one is computed by reducing a high order model , by L/sub 2 / model reduction . In the FIR case we show that it is never better to estimate the model directly from data , compared to estimating it via L/sub 2 / model reduction of a high order FIR model . For OE models we show that the reduced model has the same variance as the directly estimated one if the reduced model class used contains the true system
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