What we do with the kernel estimation is to come up with a probability distribution function that is derived from our train data and then use this pdf to assign weights to our neighbors in a kNN approach.
Well when the bandwidths are assigned in accordance with Scott's Rule, we see that at critical regions (where the performance of different methods diverge) kernel weighted selection methods perform better than non-weighted versions. However, for the rest of the graphs, the performance of methods are very close to each other and it is difficult to draw a solid conclusion. Below are the graphs for Desharnais dataset for Triangular, Epanechnikov and Gaussian Kernels respectively.
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