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Issue No. 02 - February (1982 vol. 4)
ISSN: 0162-8828
pp: 154-157
Luc Devroye , School of Computer Science, McGill University, Montreal, P.Q., Canada.
Consider the basic discrimination problem based on a sample of size n drawn from the distribution of (X, Y) on the Borel sets of Rdx {O, 1}. If 0 < R*< is a given number, and 'n - 0 is an arbitrary positive sequence, then for any discrimination rule one can find a distribution for (X, Y), not depending upon n, with Bayes probability of error R* such that the probability of error (Rn) of the discrimination rule is larger than R* + 'On for infinitely many n. We give a formal proof of this result, which is a generalization of a result by Cover [1].

L. Devroye, "Any Discrimination Rule Can Have an Arbitrarily Bad Probability of Error for Finite Sample Size," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 4, no. , pp. 154-157, 1982.
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