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Minimum sufficient statistics

Posted on: August 27th, 2013 by
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Let X,Y be discrete finite-valued random variables with joint pmf p(x,y). Let T(x) be a function of X satisfying the Markov chain X-T(X)-Y that has the minimum cardinality of the range, |{T(x):x is in support of X}|. Let f(x) be any other function that satisfies the Markov Chain X-f(X)-Y. Show that T(x) is a function of f(x).

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