Are there any other fitting models like MDL (Minimum Description Length) and Akaike's Information Criterion (AIC)?
Thank you in advance,
Ahmad
The short answer is yes, there are quite a few more.
The longer answer is it depends a lot on what you know about the model you are trying to fit. Information-theoretic criteria like MDL and AIC make few assumptions so they are quite generic. In this class there are more, to name a few: BIC (Bayesian Information Criterion), EDC (Efficient Detection Criterion), and tests based on SURE (Stein's Unbiased Risk Estimator) are examples.
If you put in more information about your model you can get estimators that work better under nominal conditions but are of course less robust to model mismatch. To name an example: if you know that your model is superimposed by white Gaussian noise you can tune an estimator to the expected noise statistics as it is for instance done in the Exponential Fitting Test (EFT) and its variants. Recently some better tests based on random matrix theory have popped up in this area.
Likewise, a known structure in your (noise-free) data can be used to improve the estimates such as shift invariance (as in ESTER) or multilinear structures (as in multidimensional estimators such as R-D EFT, etc.).
I would recommend searching for survey papers on model order selection to get started.
Good luck,
Florian.
The short answer is yes, there are quite a few more.
The longer answer is it depends a lot on what you know about the model you are trying to fit. Information-theoretic criteria like MDL and AIC make few assumptions so they are quite generic. In this class there are more, to name a few: BIC (Bayesian Information Criterion), EDC (Efficient Detection Criterion), and tests based on SURE (Stein's Unbiased Risk Estimator) are examples.
If you put in more information about your model you can get estimators that work better under nominal conditions but are of course less robust to model mismatch. To name an example: if you know that your model is superimposed by white Gaussian noise you can tune an estimator to the expected noise statistics as it is for instance done in the Exponential Fitting Test (EFT) and its variants. Recently some better tests based on random matrix theory have popped up in this area.
Likewise, a known structure in your (noise-free) data can be used to improve the estimates such as shift invariance (as in ESTER) or multilinear structures (as in multidimensional estimators such as R-D EFT, etc.).
I would recommend searching for survey papers on model order selection to get started.
Good luck,
Florian.
Thank you very much for your help Mr. Florian, i appreciate it.
Best regards,
Ahmad
I have a few papers on the subject. Please check my RG page. It is public.
PS: be careful not to oversample (that is, do not use a sampling frequency much higher than that required to satisfy Nyquist) as the model order will increase with the sampling frequency.
In addition to the ones mentioned by other posters, there are also the deviance information criterion (DIC), focused information criterion (FIC), Hannan-Quinn information criterion (HQC), Bayesian predictive information criterion (BPIC), covariance inflation criterion (CIC), risk inflation criterion (RIC), Bayes factor, false discovery rate (FDR), Mallow's Cp, minimum message length (MML), structural risk minimization, and others. In some situations, R squared and likelihood ratios are appropriate for model selection as well.
In addition, there are methods like cross-validation and penalized regression (e.g. ridge, LASSO, nonnegative garrote) and bootstrapping, which are arguably better methods of selection than relying on specific fit criteria.
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