As I reflect back regarding the part on using "square errors" rather than "absolute errors", I do not agree totally. I guess it really depends on situations. From what I learnt in process control, we term them as "Integral square errors (ISE)" and "Integral absolute errors (IAE)" respectively (it is actually the same as summation of the square errors etc since integral is basically summing up the area under the curve). In cases where large errors are particularly unacceptable, we will use ISE so as to amplify such errors otherwise, IAE is also often used. Nevertheless, in most journal papers on process control, engineers usually used both ISE and IAE to illustrate their results.
I have also shared my old lecture notes - Classification of process models as follows (feel free to download it, it shows the various types of models as well as difference between them) :
Just some acronym used:
CSTR: Continuous stirred tank reactor
ODE: Ordinary differential equation
PDE: Partial differential equation
Group A
The unbiased estimate required for IAE are in general neither unique nor available in closed form (derivative of squared vs absolute function), and will require computationally expensive iterative solutions. Hence, it's usually convenient and efficient to use ISE. However, ISE can be sensitive to outliers, so you are right in saying that it depends on situations. Thanks for your sharing on this.
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