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The MSE could be a function of unknown parameters, in which case any estimator of the MSE based on estimates of these parameters would be a function of the data (and thus a random variable). If the estimator θ ^ {\displaystyle {\hat {\theta }}} is derived as a sample statistic and is used to estimate some population parameter, then the ...
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.
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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 ...
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
Three-component SSIM (3-SSIM) is a form of SSIM that takes into account the fact that the human eye can see differences more precisely on textured or edge regions than on smooth regions. [9] The resulting metric is calculated as a weighted average of SSIM for three categories of regions: edges, textures, and smooth regions.
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.