Algorithm AS 176 for KDE's

[johnmyleswhite]

Here's the start of an alternative KDE implementation:

using Distributions
x, smooth = kde([1., 1., 1., 2.], 512)

This code needs to get cleaned up, but it should provide a faster way to compute KDE's with Gaussian kernels than the more general purpose code currently being discussed.

There are two major bugs right now:

• Results do not integrate to 1
• There are odd interlacing effects in the results

I'll try to finish this over the next few days, but wanted to get the draft code out there for comparison with Jameson's approach -- which will probably be complete much sooner than this code will be.

[johnmyleswhite]

I've fixed the scaling problem, which was caused by an inaccurate calculation of the original histogram that gets convolved with the kernel. Still working on the interlacing problem.

[johnmyleswhite]

It would be great if someone with more familiarity with FFT's got a chance to look at this. I suspect I've made a simple mistake.

[johnmyleswhite]

This looks like it basically works now thanks to @simonbyrne's patch. I think the actual bandwidth being used is more extreme than R's, though, which leads to some oversmoothing.