Infinite divisibility under mixing - kernel density estimation

Hi all,

Can we consider a (multi-modal) kernel density estimate as a finite mixture of probabiliy distributions which would be infinite divisible?



Dark Knight
Kernal density estimates are finite mixture of probability distributions. But it may not be infinite divisible always.
Thanks Vinux for your reply.

That is precisely where I am confused... If we consider a kernel density estimate as the convolution of a kernel with the true density, then it is infinite divisible. But we know that, for instance, mixture of Gaussians are not infinite divisible, whereas a Gaussian kernel is very often used... I am confused...


Dark Knight
Kernel density estimates are not convolution of kernel with the true density.It is not the density of sum of the some random variables. It is a mixture distribution.