Selecting the best linear transfer function model

Statistics currently used to determine the best model order based on the covariance of the parameter estimates or the instrumental product-moment matrix are critically examined, particularly for their applicability to situations where input and output units differ or where there is a large or small steady-state gain. A normalization process is advocated which extends the usefulness and reliability of the statistics in these situations. A procedure for comparing determinant statistics for models of different orders is described, which simplifies current methods. The improved procedures and statistics are compared using simulated data and an instrumental variable estimation method, confirming their worth.

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