Coordinate-wise Transformation of Probability Distributions to Achieve a Stein-type Identity
نویسنده
چکیده
It is shown that for any given multi-dimensional probability distribution, there exists a unique coordinate-wise transformation such that the transformed distribution satisfies a Stein-type identity. The proof is based on an energy minimization problem over a subset of the Wasserstein space. The result is interpreted as a generalization of the diagonal scaling theorem established by Marshall and Olkin (1968).
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تاریخ انتشار 2017