Kernel density estimation: kernel MISE (vs Epanechnikov)

by Luís Marques   Last Updated August 22, 2018 21:19 PM

In most places where I've looked, it generally says that the Epanechnikov kernel is optimal for kernel density estimation (KDE), in the sense that it minimizes the mean integrated squared error (MISE). See for instance Wikipedia, which indicates that the uniform kernel has 92.9% the efficiency of the Epanechnikov kernel.

Yet, in the paper "Swanepoel, J. W. H. (1988). Mean intergrated squared error properties and optimal kernels when estimating a diatribution function" it concludes that either a uniform kernel or an exponential kernel (depending on some conditions detailed in the paper) minimize the MISE, and are therefore the optimal ones.

What explains this discrepancy?

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