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I was reading about non-parametric kernel density estimation. http://en.wikipedia.org/wiki/Kernel_density_estimation

For uni-variate where D = 1, we can write like

enter image description here

For Multivariate Kernel density estimation (KDE), more preciously for d=3 and X = (x,y,z) can we write:

enter image description here

Is this technically correct? Can any one help with this?

J Richard Snape
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jquery404
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    This is perhaps better suited on another SE site. Maybe [programmers](http://programmers.stackexchange.com/) (since it's more of a "whiteboard" question). – ryanyuyu Jun 08 '15 at 20:04
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    Since this is about the formula and not any specific algorithm solving the formula, math.SE seems like the better migration target to me. – Ixrec Jun 08 '15 at 20:07
  • My guess would be [Theoretical Computer Science](http://stackoverflow.com/questions/30717822/what-is-the-equation-for-multivariate-kernel-density-estimation-techniques#comment49493711_30717822), not Math.SE. – durron597 Jun 08 '15 at 20:21
  • I'm voting to close this question as off-topic because it should be migrated, probably to math.stackexchange.com, possibly programmers.stackexchange.com if it's really a request for an algorithm rather than an equation. – J Richard Snape Jun 10 '15 at 09:26
  • I'm voting to close this question as off-topic because it should be on Theoretical Computer Science stack exchange – durron597 Jun 10 '15 at 18:39

1 Answers1

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This is very difficult to do on your own, and you really should do this through some package. Nevertheless, the definition is:

fH(x)= 1 / n \sum{i=1}n KH (x - xi), where

  • x = (x1, x2, …, xd)T, xi = (xi1, xi2, …, xid)T, i = 1, 2, …, n are d-vectors;

  • H is the bandwidth (or smoothing) d×d matrix which is symmetric and positive definite;

  • K is the kernel function which is a symmetric multivariate density;

  • KH(x) = |H|−1/n K(H−1/2x).

jquery404
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Ami Tavory
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  • im planning to do it in python. i already tried for 1D / where d =1, but I need it for 3D data.. here what I tried http://stackoverflow.com/questions/30696741/how-to-implement-kernel-density-estimation-in-multivariate-3d any idea? – jquery404 Jun 08 '15 at 20:24
  • How about [this](http://stackoverflow.com/questions/21918529/multivariate-kernel-density-estimation-in-python)? Sorry, but you really should not (re)implement this on your own, IMHO. – Ami Tavory Jun 08 '15 at 20:29
  • yeah you are absolutely right, but i was trying to get the intuition of KDE in 3D. i was reading this page http://goo.gl/UcIjmh (section EXAMPLE 3.3). They have shown equation for 2D. Could you please help me to write that for 3D or is my one correct ? – jquery404 Jun 08 '15 at 20:33
  • Not today, sorry. When I have more time. – Ami Tavory Jun 08 '15 at 20:35