Mean squared error defined

If these M points are randomly scattered near Z(i), then the average error is near zero (positive and negative errors are equally likely), but the average square error is nonzero. An accurate Taylor expansion could be defined as one for which the root-mean-square error is less than some tolerance, Etoi,... 

Another figure of merit for the fit of a linear regression model is the root mean square error of estimate (RMSEE), defined as ... 

The mean-square errors due to slope contribution and the total mean-square errors are defined as... 

The b vector chosen by the validation procedure can be employed prospectively to predict concentrations of the analyte of interest in independent data. Similar to the calculation of RMSECV, the root mean square error of prediction (RMSEP) for an independent data set is defined as the square root of the sum of the squares of the differences between predicted and reference concentrations. 

The percentage root mean square error may be defined by (for uncentred data)... 

A commonly used error function is the root-mean-square error, which is the square root of the sum-of-square errors calculated from all patterns across the entire training file. Other error functions (cost functions) may also be defined (Van Ooyen Nienhuis, 1992 Rumelhart et al., 1995), depending on the particular application. 

Residual Mean Square, RMS or ( mean square error, expected squared error). The estimate s of the error variance o, defined as ... 

In our example of three treatment groups there are three pairwise comparisons of interest. Therefore, each pairwise comparison will be tested at an a level of 0.05/3 = 0.01667. This a level will require defining a critical value from the t distribution with 12 (that is, 15 - 3) df that cuts off an area of 0.00833 (half of 0.01667) in the right-hand tail. Use of statistical software reveals that the critical value is 2.77947. From inspection of the ANOVA table presented as Table 11.4 the within-samples mean square (mean square error) can be seen to be 1. The final component needed for the MSD is ... 

Normalized root mean square error, denoted as NRMSE (or normalized root mean square deviation, NRMSD), is defined dividing RMSE (or RMSD) by the range of the response variable ... 

Note. The terms mean square error, root mean square error, mean square deviation, root mean square deviation, and expected square error are also often defined using the word squared instead of the word square . 

Root mean square error in prediction (RMSEP) (or root mean square deviation in prediction, RMSDP). Also known as standard error in prediction (SEP) or standard deviation error in prediction SDEP), is a function of the prediction residual sum of squares PRESS, defined as... 

When comparing different lossy image compression algorithms one usually desires the compressed image to be of the same visual quality as the original image. The most common measure of quality is the mean square error (MSE) or distortion defined as ... 

Now define = wtf -I- (1 — w)t where w is to be determined so as to make the mean square error of a minimum. We then have... 

Results of section 7 proved that it was reasonable to not try to estimate indicator on an unlearned space. However it was found that the estimation error is function of the distance of the learning space. Thus it may be possible to authorize the indicator estimation if the data are not far from the learning space according to a predefined threshold. The One class SVM theory enables to define the vahdity domain in function of the learning data set. The increasing error study should help to determine the threshold corresponding to the domain expansion authorized in order to keep the mean squared error, MSE, imder a value which does not disturb the detection process. 

We define then the reduced root mean square errors A,.( m) and A (r, m) in position and velocity. 

Common PMs include (1) the average (or mean) absolute error (or deviation), [210, - Dj ]/N, where the sum is over i and N is the number of cases (2) the average (or mean) squared error (sometimes called PRESS or SEC ), 2(0, -Di)VN (3) the root-mean-square error (RMSE), which most authors take as [2(0, - D,2 )/N]i/2 but which others take as [2(Oj - D,)2]t/2/>f. gnJ (4) Pearson product-moment correlation coefficient, or simply the correlation coefficient. This coefficient is defined as follows ... 

In the simulated annealing in the present method, (0,rt) phase of each paxel in the hologram elements is flipped 0 to It or vice versa as a perturbation. Then the cost function is calculated and the perturbation is accepted or not according to the simulated annealing. The cost function defined here is the mean-square error between the original image intensity to be reconstructed and the estimated one and is given by... 

The MSB in Equation 23.16 represents the mean squared error of the image and is defined... 

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