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Thread: Infinite divisibility under mixing - kernel density estimation

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    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?

    Thanks.
    Cluster

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    Kernal density estimates are finite mixture of probability distributions. But it may not be infinite divisible always.
    In the long run, we're all dead.

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    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...

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    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.
    In the long run, we're all dead.

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