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The MAE is conceptually simpler and also easier to interpret than RMSE: it is simply the average absolute vertical or horizontal distance between each point in a scatter plot and the Y=X line. In other words, MAE is the average absolute difference between X and Y.
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).
Asymptotic normality of the MASE: The Diebold-Mariano test for one-step forecasts is used to test the statistical significance of the difference between two sets of forecasts. [ 5 ] [ 6 ] [ 7 ] To perform hypothesis testing with the Diebold-Mariano test statistic, it is desirable for D M ∼ N ( 0 , 1 ) {\displaystyle DM\sim N(0,1)} , where D M ...
When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.
The significant difference between the estimation problem treated above and those of least squares and Gauss–Markov estimate is that the number of observations m, (i.e. the dimension of ) need not be at least as large as the number of unknowns, n, (i.e. the dimension of ).
Their difference is divided by the actual value A t. The absolute value of this ratio is summed for every forecasted point in time and divided by the number of fitted points n . MAPE in regression problems
The absolute difference between A t and F t is divided by half the sum of absolute values of the actual value A t and the forecast value F t. The value of this calculation is summed for every fitted point t and divided again by the number of fitted points n.
[3] [4] For 16-bit data typical values for the PSNR are between 60 and 80 dB. [5] [6] Acceptable values for wireless transmission quality loss are considered to be about 20 dB to 25 dB. [7] [8] In the absence of noise, the two images I and K are identical, and thus the MSE is zero.