This doesn't make sense to me. Any time you want a reduced order model, you will get error. For example: - Say I have data which is perfectly sinusoidal, with

This doesn't make sense to me. Any time you want a reduced order model, you will get error. For example: - Say I have data which is perfectly sinusoidal, with an dc bias. I can fit a line a to this data, which will approximate the bias (or be exactly the bias if the data is over an integer number of cycles). - I want to fit a plane to a curved surface - I want to fit a low order transfer function to a high order system. - I want to model a system with friction as a system with no friction. Fitting parameters in all of these situations will result in a non-zero residual. But assuming that is due to randomness is not useful.