Infinite divisibility under mixing - kernel density estimation

#1
Hi all,

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

Thanks.
Cluster
 

vinux

Dark Knight
#2
Kernal density estimates are finite mixture of probability distributions. But it may not be infinite divisible always.
 
#3
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...
 

vinux

Dark Knight
#4
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.