All the ANN types in the present study were trained with the appropriate algorithms until reaching the lowest possible

root-mean-square error (RMSE) on the validation set - a part of the learning set used for preventing overtraining.

The following measures of quality of the time series predictions were used to evaluate the results: mean absolute error (MAE), mean square error (MSE),

root-mean-square error (RMSE), mean absolute percentage error (MAPE), directional accuracy (DAC), relative absolute error (RAE), and root relative squared error (RRSE).

The test results demonstrated that the proposed algorithm had a higher accuracy compared to the traditional algorithms, and its mean absolute error and

root-mean-square error were significantly smaller than those of the traditional algorithms.

All features are model calibration sets for unit variance and the root-mean-square of calibration ([RMSEC.sup.a]),

root-mean-square error of cross-validation ([RMSECV.sup.b]), determination coefficient of calibration sets ([R.sup.2.sub.cv]), and determination coefficient of cross-validation sets ([R.sup.2.sub.cv]).

To make the unit of the results obtained from (9) being the same as the unit of the DOA, the square root of the the variance (standard deviation), which is equal to the

root-mean-square error due to the mean value of the DOA estimation error being zero, is used in Figure 1.

The results of JJA, 2005, for CORDEX-SA show a higher spatial correlation (SCORR) (0.74) with the lowest

root-mean-square error (RMSE; 3.17 mm [d.sup.-1]) for SSBC_New when compared with SSBC_Def and R-2.

To show accurately the difference between synthetic models and reality traces, we use

root-mean-square error (RMSE) to identify the difference degree in Fig.

For PLS and RBFEI-PLS, the number of latent variables is determined according to the

root-mean-square error of five-fold cross-validation (RMSECV).

r = Sample correlation coefficient [C.sub.v](RMSE) = Coefficient of variation of the

root-mean-square error n = Sample size Subscripts s = simulation variable m = measured variable i = index REFERENCES

For each trial, we calculated the

root-mean-square error between the target and the actual position of the virtual object.

The

root-mean-square error [8] between the input and output image is defined as:

The data were a good fit to the model (Chi square equaled 63.32, with degrees of freedom equal to 73, sample size equal to 177, p value equal to .78, and the

root-mean-square error of approximation equal to 0.0).