## 7 Results
As expected without contamination, the EK82 method was the best with most criteria presenting angles close to zero, but there was a wide multiplicity of ranks with an approximately equal result. For this reason, in this specific situation, it is recommended to take the lowest rank (three) that corresponds to the \(W_{m(Max)}\) criterion. With the change in criterion, at the maximum level of contamination (20%), EK84 (with \(W_{m}\) and \(W_{m(Max)}\)) again showed the best performance selecting rank three to obtain the lowest critical angle. Results that we did not expect occurred at the other contamination levels (5 and 10%), EK84 was surpassed by EK82 (with \(W_{m50(Max)}\)) and EK01 (with \(W_{m75}\)) with the smallest angles. These last results compared to those obtained from the simulations suggest that the methods can become unstable if the rank is selected taking into account these angles. Because of this situation, it is suggested in practice to repeat the procedure several times when the contamination level is between 5 and 10%. We repeated the procedure ten times for these two percentages of outliers (not shown) and found that, for the wine matrix, the lowest average of the critical angles was obtained with EK01 (using \(W_{m75}\)). A short comment now follows regarding the distributional and computational aspects. The methods considered in this research depend on (r)SVDs; therefore, they are distribution-free and only require that the dataset under study can be written in a matrix form. On the other hand, the computational characteristics of the algorithms depend on several factors, such as implementation used, computer characteristics, matrix dimension, correlation  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline \multicolumn{11}{c}{**Process Statistics for the Real Dataset**} \\ \hline \multicolumn{11}{c}{**Outliers = 0\%**} & \multicolumn{1}{c}{**Methods**} & \multicolumn{1}{c}{**Outliers = 10\%**} & \multicolumn{1}{c}{**Methods**} & \\ \hline Criterion & EK01 & R & EK13 & R & EK82 & R & EK84 & R & Criterion & EK01 & R & EK13 & R & EK82 & R & EK84 & R \\ \hline PRESS & 185 & 9 & 66 & 7 & 162 & 4 & 493 & 4 & PRESS & 598 & 1 & 79,846 & 1 & 124,788 & 1 & 500 & 5 \\ PRESS75 & 185 & 9 & 66 & 7 & 53 & 7 & 493 & 4 & PRESS75 & 598 & 1 & 79,846 & 1 & 124,788 & 1 & 514 & 6 \\ PRESS50 & 280 & 5 & 66 & 7 & **24** & 9 & 492 & 7 & PRESS50 & 598 & 1 & 79,846 & 1 & 124,788 & 1 & 500 & 5 \\ \(W_{m}\) & 300 & 4 & 469 & 1 & 455 & 1 & 491 & 3 & \(W_{m(Max)}\) & 188,330 & 5 & 250,402 & 4 & 343,767 & 4 & 500 & 5 \\ \(W_{m}\)(Max) & 280 & 5 & 231 & 3 & 222 & 3 & 491 & 3 & \(W_{m(Max)}\) & 188,330 & 5 & 250,402 & 4 & 343,767 & 4 & 500 & 5 \\ \(W_{m}\)(Max) & 280 & 5 & 129 & 5 & 162 & 4 & 493 & 4 & \(W_{m(Max)}\) & 611 & 2 & 79,846 & 1 & 124,788 & 1 & 499 & 5 \\ \(W_{m(Max)}\) & 280 & 5 & 66 & 7 & 53 & 7 & 493 & 4 & \(W_{m(Max)}\) & 317,830 & 8 & 79,846 & 1 & 124,788 & 1 & 499 & 5 \\ \(W_{m(Max)}\) & 300 & 4 & 94 & 6 & 82 & 6 & 493 & 4 & \(W_{m(Max)}\) & 147,451 & 4 & 79,846 & 1 & 124,788 & 1 & 499 & 5 \\ \(W_{m(Max)}\) & 300 & 4 & 38 & 9 & **24** & 9 & 493 & 4 & \(W_{m(Max)}\) & 317,830 & 8 & 79,846 & 1 & 124,788 & 1 & 499 & 5 \\ \hline \multicolumn{11}{c}{**Outliers = 5\%**} & \multicolumn{1}{c}{**Methods**} & \multicolumn{1}{c}{**Outliers = 20\%**} & \multicolumn{1}{c}{**Methods**} & \multicolumn{1}{c  
structure and outliers' quantity and location. This last aspect is important because, in some cases, the location and quantity of outliers may or may not favor the calculations and the rapid convergence of the iterative procedures that involve the calculation of an (r)SVD. To present the reader with an idea of the times of each algorithm, we analyzed one of the previously simulated matrices and the real data matrix of red wines on a personal computer with an Intel(R) Core(TM) i7-8550U, CPU 1.80 GHz 1.99 GHz and 8 GB of RAM installed. Table 5 shows the comparison of times of the different cross-validation methods.