Abstract
We consider the problem of mappingX→Y, whereX andY have given distributions, so as to minimize the expected value of ∣X–Y∣2. This is equivalent to finding the joint distribution of the random variable (X, Y), with specified marginal distributions forX andY, such that the expected value of ∣X–Y∣2 is minimized. We give a sufficient condition for the minimizing joint distribution and supply numerical results for two special cases.
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Communicated by D. Q. Mayne
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Knott, M., Smith, C.S. On the optimal mapping of distributions. J Optim Theory Appl 43, 39–49 (1984). https://doi.org/10.1007/BF00934745
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DOI: https://doi.org/10.1007/BF00934745