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In control theory, the RMSE is used as a quality measure to evaluate the performance of a state observer. [ 10 ] In fluid dynamics , normalized root mean square deviation (NRMSD), coefficient of variation (CV), and percent RMS are used to quantify the uniformity of flow behavior such as velocity profile, temperature distribution, or gas species ...
The use of the MAPE as a loss function for regression analysis is feasible both on a practical point of view and on a theoretical one, since the existence of an optimal model and the consistency of the empirical risk minimization can be proved.
This page was last edited on 25 December 2021, at 09:39 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was later discussed, modified, and re-proposed by Flores (1986).
This page was last edited on 21 December 2024, at 20:13 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
This is in contrast to RMSE which involves squaring the differences, so that a few large differences will increase the RMSE to a greater degree than the MAE. [ 4 ] Optimality property
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
This page was last edited on 15 November 2024, at 14:41 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.