Solved – How to choose a kernel for KDE

data visualizationdistributionskernel-smoothingnonparametric

There are a lot of kernels available for a univariate KDE. R uses normal by default, but the efficacy discussion seems to support the use of Epanechnikov. What should influence kernel choice for univariate exploratory analysis?

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This is not really a data visualization question. The information is fairly readily available online, eg http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0405/MISHRA/kde.html

mentions using AMISE to select bandwidth, same approach for kernels could be used. But for EDA, you would want to work like the recommendation for histograms, re-plot with different binwidths to learn different things in the data. Sometimes using a different kernel may be helpful. The normal kernel is generally useful, and I think the bandwidth is more important than the actual kernel.

I would suggest adding tags: distributions, nonparametric. Possibly get better answers under these topics.

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Solved – Choosing a bandwidth for kernel density estimators

For a univariate KDE, you are better off using something other than Silverman's rule which is based on a normal approximation. One excellent approach is the Sheather-Jones method, easily implemented in R; for example,

plot(density(precip, bw="SJ"))

The situation for multivariate KDE is not so well studied, and the tools are not so mature. Rather than a bandwidth, you need a bandwidth matrix. To simplify the problem, most people assume a diagonal matrix, although this may not lead to the best results. The ks package in R provides some very useful tools including allowing a full (not necessarily diagonal) bandwidth matrix.

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Solved – Choosing a bandwidth for kernel density estimators

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