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| Titel |
Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature |
| VerfasserIn |
T. Chai, R. R. Draxler |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1991-959X
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| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 7, no. 3 ; Nr. 7, no. 3 (2014-06-30), S.1247-1250 |
| Datensatznummer |
250115640
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| Publikation (Nr.) |
 copernicus.org/gmd-7-1247-2014.pdf |
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| Zusammenfassung |
| Both the root mean square error (RMSE) and the mean absolute error
(MAE) are regularly employed in model evaluation studies.
Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator
of average model performance and might be a misleading indicator of
average error, and thus the MAE would be a better metric for that
purpose.
While some concerns over using RMSE raised by Willmott and Matsuura (2005) and
Willmott et al. (2009) are valid, the proposed avoidance of RMSE
in favor of MAE is not the solution. Citing the aforementioned papers,
many researchers chose MAE over RMSE to present their model evaluation
statistics when presenting or adding the RMSE measures could be more beneficial.
In this technical note, we demonstrate that the RMSE is not
ambiguous in its meaning, contrary to what was claimed by
Willmott et al. (2009). The RMSE is more appropriate to represent model
performance than the MAE when the error distribution is expected to
be Gaussian. In addition, we show that the RMSE satisfies the
triangle inequality requirement for a distance metric, whereas
Willmott et al. (2009) indicated that the sums-of-squares-based
statistics do not satisfy this rule. In the end, we discussed
some circumstances where using the RMSE will be more beneficial.
However, we do not contend that the RMSE is superior over the MAE.
Instead, a combination of metrics, including but certainly not limited
to RMSEs and MAEs, are often required to assess model performance. |
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