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Instead of solving this difficult optimization problem, Gönen et al. estimated kernel weights by using the gating function.
Subpopulations were formed by decreasing order of the kernel densities, starting with the largest estimated kernel density (by setting method = 6 at PROC MODECLUS).
The approach is based on the combination of robustness analysis, moment independent robustness indicator, and estimated kernel conditional densities.
The estimated kernel density for the values of the area under E R K∗ signal is shown in Fig. 12 a: it has a mean, a variance and a mode presented in Table 2.
If in addition the set of all current locations (in a region) of herds with pigs is available, the estimated kernel can be used to measure the expected amount of neighborhood transmission by calculating a local reproduction ratio R hi for each herd i.
The violin plot is a modification of the box plot that adds plots of the estimated kernel density to the summary statistics displayed by box plots [ 33], incorporates a marker for the median of the data, a box indicating the interquartile range, and spikes extending to the upper- and lower-adjacent values; overlaid is a density plot.
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Furthermore, the estimated kernels are shown in Figure 4.
For speed considerations, we estimate kernel density over 300 equally spaced points within the interval [ max (− 5, min (x ) ), min (5, max (x ) ) ].
The distribution of each CPR variable was estimated by kernel density estimation with a Gaussian kernel function and plotted by treatment arm.
First, the distributions of cross-validation prediction scores for negative and positive examples were estimated using kernel density estimation as implemented in R (R Development Core Team, 2008).
In a second step, the ATE is estimated by kernel matching using the Epanechnikov kernel with a bandwidth of 0.06.
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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