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I was reading about non-parametric density estimation when I found out about Kernel Density Estimation (KDE) and Parzen window estimation. Although the text book states both are the same, the equation form seems to be different:

For Kernel density estimation (KDE) 3D data

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For Parzen-window estimation in 3D data

enter image description here

Can any one help with this?

Archie
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jquery404
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    I think these terms are used interchangeably (depending on discipline). The two equations are clearly the same. Here, $K(x)$ is your kernel function in 3 dimensional space. The $k$ function will typically be a PDF. – Luca Jun 03 '15 at 08:06
  • @Luca, but 1/h^3 is outside kernel function in KDE, which will be multiplied once, but in case of parzen-window it is inside. isn't that mean in parzen-window kernel function being multiplied by some fraction (1/h^3) each iteration? – jquery404 Jun 03 '15 at 08:09
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    You can take $1/h^3$ outside the summation. It is a constant. – Luca Jun 03 '15 at 08:11
  • Multiplying each term in a summation by some fraction is the same as multiplying the sum of terms by that fraction. $\frac {1}{2} \times 2 + \frac{1}{2} \times 4= \frac{1}{2}\times (2+ 4)$. – Scortchi - Reinstate Monica Jun 08 '15 at 00:52

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