Abstract
The problem considered is that of identifying two finite dimensional probability distributions G and H from their convolution, F = G * H, when all that is known about them is that H is symmetric. This problem arises in looking for hidden structure in multivariate data, for example. It is shown that one can always find a solution in which G has no nondegenerate symmetric convolution factor. However the solution is not unique in general. Examples of such “completely asymmetric” distributions are given. Existence and examples rather than estimation are the focus of the paper.
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Ellis, S.P. Blind Deconvolution When Noise is Symmetric: Existence and Examples of Solutions. Annals of the Institute of Statistical Mathematics 54, 758–767 (2002). https://doi.org/10.1023/A:1022459217720
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DOI: https://doi.org/10.1023/A:1022459217720