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(E_{k2}) gives the (E_k) values obtained from robust residuals based on MCD estimators.
(E_{k3}) gives the (E_k) values obtained from weighted residuals based on the MCD estimators.
In Tables 1 and 2: (E_{k1}) gives the (E_k) values obtained from the classic residuals based on classic estimators.
The variance of the residuals based on the standard deviations of the quality characteristics x and y that are calculated by Eqs.
Because the RMS of travel time residuals based on the three-dimensional model are smaller than those based on the JMA2001 model, we used hypocenter locations derived from the three-dimensional model in further analysis.
While equal weight is given to all residuals in the first step, different weights can then be attributed to the residuals, based on the magnitude of the observed concentration or the chemical identity of the compound observed.
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CRC uses the minimum reconstruction residual based on collaborative representation as the decision rule.
In the result of analysis of residual based on histogram approximates the standard level, the residual has a mean value 3.32 × 10 ≈ 0 and std.
Hence, we present a new residual based on the CEV weights as follows: z^{prime}_{i} = frac{{W_{2i} - {text{E}}(W_{2i} )}}{{sqrt {{text{Var}}(W_{2i} )} }}, (28 where ( E(W_{2i} ) ) and ( {text{Var}}(W_{2i} ) ) are the mean and variance of observations.
Let A be the n×n diagonal matrix with the ith entry given by ({r_{i}^{2}} 1-h_{textit {ii} 1-h_{textitit {ii}}}), where r i is the ith residual based on the ordinary least squares estimator.
The Pearson residual, based on the estimated mean and variance compared with the observations, and the Anscombe residual, built only with the estimated mean and the observations, may be inspected vs. λ or or time to detect misspecifications.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com